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E^V. iEANTLET YOEK,

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liortb Carolina State Library
Raleigh

THE

MAN OF BUSINESS

—AND-

RAILROAD CALCULATOR

CONTAININa

8VCH PARTS OF ARITHMETIC AS HAVE A SPE-
CIAL APPLICATION IN BUSINESS
r TRANSACTIONS,

— AND ALSO-

ABRIDGED FORMS OF OPERATION ; TOGETHER WITH

SUCH PROOFS AS ARE REQUISITE TO TEST

THE ACCURACY OF EACH OPERATION.

BY REV. BRANTLEY YORK, D.D.

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^ J ^ ^ o ' ' * * '' '^ ,"• ^ t , 6 ' y' J 3 J J :> 5 * -♦

:> J ^ 'T6-' WHICH ARE APPENDED A FEW OP THE

PLAm-fei^ ' 'LEC^A^L ''-FOR MS

NECESSAEY IN OKDINARY BUSINESS,

PREPARED BY

RICHARD WATT YORK, A. M.

Attorney and Counsellor at Law.
RALEIGH :

JOHN NICHOLS A CO., BOOK AND JOB PRINTERS,
1873.

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CONTENTS.

Preliminaries, "^^^^;

Numbers, ^

Methods of expressing numbers, t

Arabic Method, I

Fundamental or Ground Rules, 7
bigns by which the operations are

indicated, r.

Axioms, n

Ground Eules-Methods of proof, 9
Subtraction, -r,

Multiphcation, iV

Division, -jo

Practical rules deduced from the

foregoing principles, 13

Denominate Numbers 13

Reduction of Denominate Num-
bers,
Enghsh Money,

^w''-^^?°'^ °^ Commercial
Weight,

Troy or Mint Weight,

Apothecary's Weight,

Linear or Long Measure,

Mariner's Measure,

Cloth Measure,

Surface or Square Measure

Surveyor's or Engineer's Measure

Cubic or Solid Measure,

Wine Measure,

Ale or Beer Measure,

Dry Measure,

Time Measure,

Circular Measure,

Table of particular.

Books and Paper,

Properties of numbers,

Factoring,

Rules for Factoring,

The greatest Common Divisor or

Measure,
Solution of Problem,
The least Common Multiple
To find the least Common Mul-
tiple,
Problems for Solution

15
16
17

17
18

18|

isl

191

27
28

Fractions,
Propositions,

Different kinds of Fractions,
Reduction of Fractions,
Decimal Fractions,
Reduction of Decimals,
Decimal Currency,
Metahc Currency,
Duodecimals,
Analysis,

Abridged Forms of Operations-
General Rules,
Table of Aloquot Parts,
Special Rules,

The Extended Multiphcation Ta-
ble,
Per centage,

The Basis and Rate per cent, be-
ing given to find the P'r Centage.
The Rate p'r cent, and Per Centape

given to find the Basis,
The Basis and Per Centage given

to find the Rate,
The Basis and Rate per cent, given
I to find the Amount,
The Basis and Rate per cent, given
j to find the difference.
Amount and Rate per cent, to find

the Basis,
Difference and Rate per cent.

given to find the Basis,
Basis and Resultant number given

to find the Rate per cent.
To find what Per Cent, a
number is of another
number.
Formulas of Per Centage,
Rate Per Cent, above 100,
Basis and Rate per cent, given to

find Per Centage,
Basis and Rate per cent, given to

find Amount,
Amount and Rate per cent, given

to find the Basis,
Partnership or Company business,

Pag

given
given

e.
'30
31
32
33
36
38
38
39
39
40

42
43
45

47
■51

59
60
60

61
62

CONTENTS.

Page.

Baukruptcy or lusolvency, (55

Assessing Taxes, 6(5

Commissiou, Brokerage & Stocks, (>8

lusnrauce, 70

Profit and Loss, 71

Exchange, 72

The form of Inland Draft, 73

Barter, 73

Custom House Business. 75

Per Centage involving Time, 77

Simi)le Interest, 77
Principal. Rate per cent., and

Time given to find the Interest, 77
Method of computing Interest on

English money, 81
Interest, Bate i^er cent., and Time

given to find the Principal, 83
Principal, Interest, and Rate per

cent, to find Time, 84
Principal, Int'rest, and Time given

to find Rate per cent., 84

Partial Payments, 85

Formulas, 86

Compound Interest, 87

True Discount, 89

Bank Discount, 90

Page.
Equation of Payments, 91

Find the Time for any Principal

at a given rate to double itself, 93
Mensuration, 93

Mensuration of Surfaces, 94

Land Measure, 95

Flooring, Ceiling, Roofing and

Carpeting, 98

Plasterer's, Painter's, Paver's and

Carpenter's Work, 100

Board Measure, 101

Mensuration of Log or Ruond

Timber, 103

Mensuration of Solids or Volumes, 104
Crib and Box Measure, 105

Mason's and Bricklayer's Work, 106
Heights and Depths measured by

the velocity of falling bodies, 107
Distances measured by the velo-
city of Sounds, 109
Gauging Casks, 109
Miscellaneous, 111
Cause and Effect, 111
Rvile for Extracting the Square

Root, 115

Legal Forms,

120, 147

PREFACE.

An ardent desire to be useful, has prompted the author
to prepare this work for publication. If this object be at-
tained, he will have reached the height of his ambition.

Long experience in teaching, and attentive observation,
have convinced him that this or some similar work is need-
ed ; it is a fact patent to business men generally that not a
few of those who go into any of the business departments of
the country, notwithstanding they may have gone through
an academical course of instruction, have to learn how to
transact business efficiently, after they engage in it. How
far this work may go in supplying the wants of any com-
munity in this respect, is not for the Author to decide ; but
it is left for a discerning and appreciating public to deter-
mine.

Dispatch and accuracy are prime qualities in all business
transactions: time is not only money; but, in many res*
pects, it is more. In the Man of Business and Rail Road
Calculator, the means are ample for acquiring both these
qualities; the former may be acquired by attentively study-
ing the abridged forms of operation ; the latter by applying
the tests of accuracy as exhibited in the proofs of the vari-
ous operations.

This work is not intended to supercede any Arithmetic
in use ; but to aftord the means in a condensed form for ac-
quiring a business education ; it, however, contains a suffi-

4 PREFACE.

cient number of arithmetical principles and 7'ules for the so-
lution of all the questions or problems which it contains.

Though care has been taken to avoid error both in theory
and practice, yet doubtless some will be found, and the
Author will be obliged to any one discovering any errors in
it, to promptly point them out to Mm.

This book is not intended for the use of private learners
only ; but also for schools — in short, for all who may see
proper to use it.

In the preparation of this work, various Authors have
been consulted ; but the Author deems it unnecessary to
specify any.

Had the Author possessed the advantage of vision, some
of the forms, perhaps, would have been arranged to better
advantage; but the book, such as it is, is now offered to a
.discriminating and indulgent public.

THE AUTHOR.

RurFiN Badqek, March 5th, 1873.

PRELIMINARIES.

Definitions^ Principles^ and Rules.

Article I. 1. Quantity is anything which is susceptible
of measurement.

2. Arithmetic is the science of numbers, and the art of
computation.

3. A unit is a single thing denoting a whole, and is eith-
er abstract or concrete.

4. An abstract unit does not express the kind of unit ; as,
one, two, &c.

5. A concrete unit expresses the kind of unit ; as, one ap-
ple, one pound of tea<, etc.

NUMBERS.

II. 1. A nurnber is a unit or a collection of units; as, one,
two, six, etc.

3. An abstract number expresses number simply, irrespec-
tive of the kind of unit.

3. A concrete or denominate number expresses the kind sf
unit designated ; as, two pounds, five yards, etc.

4. A simple number expresses one kind, whether abstract
or concrete.

METHODS OF EXPRESSING NUMBERS.

ni. 1. There are three methods of expressing numbers,
viz:

6 THE MAX or BUSINESS

1. By written or printed imrds ; as, four, nine, etc.

2. By capital letters called the Roman Method. For this
purpose, seven capital letters are used, viz: I, one, V, five,
X, ten, L, fifty, C, one hundred, D, five hundred, M, one
thousand.

3. By figures called the Arabic Metlwd ; as, 1, 3, 3, 4, etc.

IV. There are four principles involved in expressing
jQumbers by the Roman Method.

1. A letter of less value, prefixed to one of greater value,
subtracts its value from the greater; as, IX=nine,

2. A letter of less value, annexed to one of greater value,
adds its value to the greater ; as, XI==eleven.

3. A letter rejDeated, repeats its value; as, C C, =two
hundred.

4. A dash placed over a letter, multiplies it by one thou-
sand ; as T=five thousand.

Note. — This method is now principally used to number volumes, chapters
of books, primary rules, to mark the hours on the faces of clocks and watch-
es, dates engraven on tomb-stones, and generally to express the number of
dollars on bank bills.

EXERCISES.

V. 1. Express by the Roman Notation the following
numbers, 4, 15, 19, 30, 34, 40, 49, 50, 60, 72, 300, 95, 500,
800, 1000, 1200, 150, 600, 1873.

2. Express the following Roman Notation in figures,
XII, XIII, XYI, XX, XXVII, XL, LXV, LXXIII, CCC,
XC, D, DCCCC, MD, MDCC, M, MDCCC, LXXIII.

ARABIC METHOD.

VI. 1. There are ten characters used in the Arabic Meth-

AND EATL ROAD CALCULATOR. 7

od, called figures, viz: 1, 3, -8, 4, 5, 6, 7, 8, 9, 0. Nine of
these are called digits or significant figures, the other is
called naught or cipher.

2. Figures have two values, a positive and a local value.
A figure has a positive value, when it stands alone or oc-
cupies the unit's place; thus 5 expresses simply five units;
but, if another figure he v/ritten on the right hand of it, its
value becomes local ; thus 55 ; its value now is fifty units or
five tens, tens being the scale expressing the law of increase
and decrease.

3. All the operations in Aritlmietic are performed by
variously combining these figures.

FUNDAMENTAL OR GROUND RULES.

VII. 1. Notation and Numeration, Addition, Subtrac-
tion, Multiplication and Division are called fundamental or
ground rules; because some of them underlie or are the
foundation of all other operations.

SIGNS BY WHICH THE OPERATIONS ARE INDICATED.

VIII. 1. Two short parallel lines (==) equal to, are
placed between two numbers or quantities of equal value ;
as, 2+5=7.

2. An upright cross (-f) called plus, is the sign of Addi-
tion; as, 2-f4=6.

3. A short horizontal line ( — ) called minus, is the sign of
Subtraction. The minuend is written on the Ze/ihand, and
the subtrahend on the right; as 8 min. — 2 sub. =6.

S THE MAN OF BUSINESS

4. An oblike cross (X) called times or into, is the sign of
Multiplication; as, 5X4=20.

5. The sign of division is a horizontal line drawn be-
tween two dots (-^) called *'6y." The Dividend should be
written on the left, and the Divisor on the right hand. Ex.
24-|-6=4. This operation is sometimes indicated by a sin-
gle line with the Dividend written above, and the Divisor
below; thus, ?1=4, or by a curve and horizontal line uni-
ted ; thus 6 /21.

6. The sign of aggregation, a parenthesis, ( ), including
several numbers or a vinculum, , drawn over them, in-
dicates that the value of the expression, is to be used as a
single number. Thus (12-f3)X5 indicates that the sum of
12 and 3, is to be multiplied by 5 ; and 10-)-(8 — 2)-4-2, indi-
cates that the difference between 8 and 2, divided by 2, is
to be added to 10.

7. The sign of a conclusion, is three dots placed thus (. *.)
called tlierefore.

AXIOMS.

IX. The operations of Arithmetic as a branch of Mathe-
matics, are based upon certain axioms. An axiom is a self-
evident truth of which there are several kinds as follows:

1. If the same quantity or equal quantities, be added ta
equal quantities, the sums will be equal.

2. If the same quantity or equal quantities be suMracted
from equal quantities, the remainders will be equal.

3. If the same quantity or equal quantities be addedj to
unequal quartities, the sums will be unequal.

AND RAIL ROAD CALCULATOR. ^

4. If the same quantity or equal quantities be subtracted
from unequal quantities, the remainders will be unequal.

5. If equal quantities be multiplied by the same quantity
or equal quantities, the products will be equal.

6. If equal quantities be divided by the same quantity or
equal quantities, the quotients will be equal.

7. If the same quantity be both added to and subtracted
from another, the value of the latter will not be changed.

8. If a quantity be both multiplied and divided by the
same quantity, its value will not be changed.

9. If two quantities be equally increased or diminishedj
the difference will not be changed.

10. Quantities which are equal to the same quantity, are
equal to each other.

11. Quantities which are like parts of equal quantities,
are equal to each other.

12. The whole of a quantity, is greater than any of its parts.

GKOUND RULES — METHODS OF PROOF.

X. 1. Notation is the expression of numbers, whether by
words, letters or figures.

2. Numeration is reading figures correctly in their pioper
order, of which there are two methods. The first is called
the French Method, in which the figures are grouped togeth-

Mill. Thous. Units.

er by threes, called periods. Thus 555,555,555. The sec-
ond is called the English Method, and each group contains
six figures, except the left hand period which may contain
less. The former is decidedly preferable.

10 THE MA-N OF BUSINESS

XI. Addition is the operation by which several numbers
e coUec
Ex., 325

?ire collected into one aggregate amount or whole

Operation.

413

136

946 Amount.

621 Second Amount.

325 Top line, remaining Part.

946 Proof = First Amount.
Now since all the parts are equal to the whole, if we sepa-
rate any one part ; as the top line for instance, adding the
other parts, the second amount will not be equal to the first
(axiom 12) ; again, if we add the second amount to the part
separated, it will be equal to the first amount which is the
proof of the operation, (axiom 13). This process may be
facilitated by performing the operation in the opposite di"
jcection, though less scientific.

SUBTRACTION.

XII. Subtraction is an operation by which the difference

min. sub. rem.

of two given numbers, is determined. Ex. 24 — 8=16.
Proof, 8+16=24. Second Method, or 24—16=8. Now
since 24 has been diminished by 8, it follows, if 8 be added
to the difference, (16), the amount will be 24, equal to the
minuend (see axiom 1). Hence the rule for proving sub-
traction.

AND RAIL ROAD CALCULATOR. 11

Add the remainder and subtrahend^ and their sum will he
equal to the minuend, or suMract the difference from the minu-
end^ and the remainder will be equal to the subtrahend. See
the above example.

MULTIPLICATION.

XIII. Multiplication is an operation by which one given
factor is repeated as many times as these units in another
given factor.

Remark 1. The larger factor or number is generally call-
ed the multiplicand, the less is generally called the multiplier.,
and the result of the operation is called the product.

Remark 2. If the multiplier is a unit, the product will
be equal to the multiplicand, if the multij)lier is more than
a unit, the product will be as many times greater than the
multiplicand, as there are units in the multiplier; but, if
the multiplier is a fraction or less than a unit, the product
will be less than the multiplicand.

Note. — The different positions of the factors will make no
difference in the result. Hence convenience or ly may be
consulted.

Proof. — Kow since the product expresses the result of
multiplying two factors together, it follows that, if we
divide the product by either factor, the quotient will be the
other. (See axiom 8). Hence we have the following rule
for proving multiplication.

Divide the product by the multiplier., and the quotient will be
equal to the multiplicand., or divide the product by the multi-
plicand., and the quotient will be equal to the multiplier ; as ex-
hibited by the following example. What will 12 yards of
calico come to at 12%, cents a yard? Operation, 12X^2)^=
1.50. Proof, 1.50^12=121^.

12 THE MAN OF BUSINESS

Note. — There are other methods of proving multiplica-
tion ; but we deem the above sufficient.

DIVISION.

XIV. Division is the operation of finding how many
times one number is contained in another.

Eemark. The container, or number to be divided, is
called the dividend. The contained or number expressing
the number of parts into which the dividend is to be divi-
ded, is called the divisor. The number expressing the num-
ber of times which the dividend contains the divisor, is
called the quotient., and that which is sometimes left un-
divided, is called the remainder.

Rem. 2. If the divisor is a unit, the quotient will be equal
to the dividend, if the divisor contains more than a unit,
the quotient will be less than the dividend by as many times
as there are units in the divisor; but, if the divisor is a
fraction or less than a unit, the quotient will be greater than
the dividend.

Rem. 3. When the divisor is greater than the dividend,
a part only of it can be contained in the dividend ; there-
fore, the operation can only be indicated by making the
dividend a numerator of a common fraction, and the divi-
sor, the denominator. Thus let it be required to divide 3
by 5. Operation, ^.

Note. — The dividend is a product, of which the divisor is
one of the factors, and the quotient the other. Hence,
when either factor is given, the other may be found.

Proof of Division. — Now since the quotient expresses the
number of times which the dividend contains the divisor,
it follows that, if we multiply the quotient by the divisor,
adding in the remander, if any, the product will be equal
to the dividend, (see axiom 8), as exhibited in the follow-
ing example. Divide 24 by 6. Operation, 24-i-6=4. Proof,
6X4=24 or 24-f4=6, Second Method. Hence the follow-
ing rule for division.

AXD BAIL KOAD CALCULATOR. 1

Multiply the quotient hy the divisor, adding in the remainder,
If any, and the product will de equal to the dividend, or divide
the dividend lyy the quotient^ and the result will 'be the divisor.
(See note).

PRACTICAt, RULES DEDUCED FROM THE FOREQOINa
PRINCIPALS.

XV. 1. When the price of any concrete unit, is given,
and the price or amount of given number required — Multi-
ply the price hy the given number, and the product will be the
required result.

Ex. What will 34 yards of calico come to, at 14 cents a
yard. Operation, 24X14=3.36.

2. When the cost of a number of things is given, and the
price of a single concrete unit required — Divide the cost by
the given number, and the quotient tcill be the price of a single
concrete unit.

Ex. Paid 4.80 for 40 yards of cloth — required the price
of one yard? Operation, 4.80-^-40=12, the cost of a single
concrete unit.

3. When it is desired to divide a concrete number into
any number of equal parts — Divide the given number by a
7iumber whose concrete units are equal to the number of parts
desired, and the quotient will be one of the equal parts ; thus,
let it be required to divide 435 acres equally among five
persons. Operation, 435-^5=85, one of the equal parts.

DENOMINATE NUMBERS.

XVI. 1. A denominate number is a collection of con-
crete units of different denominations; as 3 ft., 4 in., 5s.,
6(3, &c.

14 THE MAK OF BUSINESS

A scale expresses the law of relation between units of dif-
ferent numbers of different kinds.

3. The scale of most denominate numbers is variable ; the
scale of the United States currency is uniform, whose radix
is ten; and the scale of duodecimals is also uniform, whose
radix is twelve.

REDUCTION OF PENOMINATE NUMBERS.

XVII. 1. Reduction of denominate numbers consists in
reducing a denominate number from one denomination to
another, without changing its value.

2. There are two kinds of reduction, viz : Descending and
Ascending; the former is affected by multiplication, the
latter by division.

3. The scale, in every case, must be the rule of operation.

^ote-. — The principal tables of denominate numbers are
here inserted, as a matter of reference, accompanied by
such explanatory notes as are deemed important.

ENGLISH MONEY.

XYIII. English or Sterling money is the currency of
England.

TABLE.

4 Farthings make 1 Penny, d.

12 Pence make 1 Shilling, s.

20 Shillings make 1 Pound, £.

Note 1. — The English coins consist of the Five-Sove-
reign piece, the double Sovereign, the Sovereign, and
half Sovereign, made of Gold ; the crown, the half crown,
florin, the shilling, the six-pence, the four-pence, the three-
pence, the two-pence, the one-and- half -pence, and the

AND EAIL ROAD CALCULATOR.

penny, made of Silver ; the penny, the half -penny, the farth-
ing, and the half-farthing, made of Copper.

Note 2. — Farthings are now generally expressed by the
fractional parts of pence; 1 farth.=3€d, &c.

JSfote 3. — The value of the English Guinea, is 21 shillings;
but the Guinea, five Guinea, h^lf Guinea, quarter Guinea,
and seven-shilling piece are no longer coined.

Note. — The value of the Sovereign is equal to 1 pound
Sterling=$4. 84 United States currency, and the value of the
Florin is equal to _L of 1 £.

AVOIEDUPOIS OR COMMERCIAL WEIGHT.

XIX. This weight is used for weighing almost any thing
except Gold and Silver and precious stones.

DENOMINATIONS.

Tb/z, Hundred- wei gilt., Quarter^ Pound., Ounce, and Dram,

TABLE

16 Drams (dr.)

make

1 Ounce, Oz.

16 Ounces

make

1 Pound, R).

25 Pounds

make

1 Quarter, Qr.

4 Quarters

make

1 Hundred-weight, Cwt.

20 Hundred-we

ight

make

1 Ton, T.

Note. — The laws of most States and common practice
have adopted the decimal 100; but formerly it was 112 the
quarter being 28, which is still the standard of the United
JStates Government in collecting duties at the custom-houses.

16 THE MAN OF BUSINESS

TROY OR MINT "WEIGHT.

XX. This weight is used to weigh Gold^ Silver^ Jewels^
and Liquors.

DENOMINATIONS.

Pound^ Oimce^ PennyweigJit^ and Grain.

TABLE.

24 Grains (gr)

make 1 Pennyweight,

pwt.

20 Pennyweight

make 1 Ounce,

OZ.

13 Ounces

make 1 Pound,

ft).

Note 1. — Diamonds and other precious stones are weighed
by what is called :

Diamond weighty of which 16 parts make 1 gr. ; 4 gr., 1
carrot. 1 gr. Diamond weight is=to 4 gr., Troy, and 1 car-
rot==3J ST. Troy. In weighing pearls, the pennyweight
is divided into 30 gr., instead of 24, so that 1 pearl gr. is=
5 gr. Troy, and 1 carrot==3l gr. Troy.

Note 2. — The *assay carrot is a term used to express the
proportional part of a weight, as expressing the fineness of
Gold ; each carrot= ^ part of the entire mass used. Thus,
pure gold is termed 24 carrot gold, and not pure is termed
18 carrot gold, 20 carrot gold, etc., ie., 18 carrot gold has
18 parts of gold and 6 parts alloy, and may be expressed
fractionally thus, ~^ |?, ~^^ etc. Each assay carrot is sub-
divided into 4 assay grains, and each assay grain, in 4 assay
quarters.

* Care should be taken not to compound the carrot of weight with assaj/
carrot.

Morth Carolina State Library
Raleigh

AND EAIL ROAD CALCULATOR.

APOTHECAEIBS WEIGHT.

XX. This weight is used in weighing medical prescrip-
tions.

DENOMLN ATIONS .

Pound^ Ounce, Dram^ Scruple^ and Grain.

TABLE.

20 Grains (gr)

make

1 Scruple,

So.

3 Scruples

make

1 Dram,

dr,

8 Drams

make

1 Ounce,

oz,

12 Ounces

make

1 Pound,

lb.

Note. — Medicines are usually bought and sold by Avoir-
dupois weight.

Note 2. — In estimating the weight of fluids. 45 drops, or a
common teaspoonful make 1 fluid dram, 12 common table-
spoonfuls, about one fluid ounce ; a wine-glassful, abouft^^g
fluid ounces, and a common teacupful about 4 fluid ounces,

LINEAR OR LONG MEASURE.

XXI. Linear measure has but one dimension, and is used
in measuring distances in every direction.

TABLE.

12 Inches (in) make

1 Foot, ft.

3 Feet make

1 Yard, yd.

53^ Yards or 16/^ Feet make

1 Rod or Poll, rd.

40 Rods make

1 Furlong, fur.

8 Furlongs or 320 Rods make

1 Mile, m.

3 Miles make

1 League, lea.

693^ Miles make 1 Degree

on the equator, deg. or o.

360 Degrees make 1 Great Circle of the earth.

THE MAN OF BUSINESS

mariner's measure.

XXII. Mariner's measure is long measure chiefly used to
measure distances at sea.

12 Lines make 1 Inch, in.

4 Inches make 1 Hand, hd,

9 Inches make 1 Span, sp.

6 Feet make 1 Fathom, fm.

120 Fathoms, make 1 Cable-length, cl.

73^ Cable-lengths make 1 Mile, mi.

1 Knot make 1 11-72 Statute-miles, st.-m.

CLOTH MEASURE.

XXIII. This measure is used in measuring dry goods,

TABLE.

1 Nail, na.

1 Quarter of a yard, qr.

1 Yard, yd.

1 Ell Flemish, e. f.

1 Ell English, e. e.

SURFACE OR SQUARE MEASURE.

XXIV. This measure is used in measuring surfaces of
all kinds.

TABLE.

144 Square Inches make 1 Square Foot, sq. ft.

9 Square Feet make 1 Square Yard, sq. yd,

303^ Square Yards make 1 Square Rod or Pole, sq. rd.

40 Square Rods make 1 Rood, r.

4 Roods make 1 Acre, a,

640 Acres make 1 Square Mile, s. m.

23^ Inches

make

4 Nails

make

4 Quarters

make

3 Quarters

make

5 Quarters

make

AND RAIL ROAD CALCULATOR. 19

Note. — Surface measure has but two dimensions — length
and breath. Hence to find the area or surface, when the
two dimensions are given, multiply them together, and the
product will be the area required.

Note. — When the area and one of the dimensions are giv-
en to find the other.

Rule, — Reduce the area to the same denomination as that of
the given dimension, then divide dp the given dimension, and
the quotient will he the other dimension in the same denomina-
tion.

Ex. A farmer wishes to lay off a two-acre lot ; he can
obtain a line in one direction 20 rods long; what must
be the length of the other? Solution. 2 acres=320 rods.
320^20=16, the other side. Proof, 16X20=320. 320-f-
160=2 acres.

surveyor's or engineer's measure.

XXV. This measure is a kind of long measure, used in
laying out roads, and running the boundaries of land.

table.

7 92-100 Inches

make

1 Link, L.

4 Rods or 66 Feet

make

1 Chain, c.

80 Chains,

make

1 Mile, m.

1 Square Chain,

makes

16 Square Rods, sq.

rd.

10 Square Chains,

make

1 Acre, a.

CUBIC OR SOLID MEASURE.

XXVIv This measure is used in measuring such bodies
■or things as have length, breath and thickness ; as timber.

stone, etc.

THE MAN OF BUSINESS

TABLE.

1728 Cubic Inches make 1 Cubic Foot, cu. ft.

28 Cubic Feet make 1 Cubic Yard, cu. yd^

40 Cubic Feet, hewn timber, make 1 Ton, t.

16 Cub. Ft. or 50 Ft., round tim., make 1 Cord Ft, c. ft.
8 Cord Feet, or 128 Cubic Ft., make 1 Cord of wood, c„.

Note. — Since cubic measure has three dimensions, in or-
der to find the solid contents of a body or capacity of rooms,
boxes, &c., multiply the three dimensions together.

Note. — A pile of wood or bark 8 feet long, 4 feet wide,
and 4 feet high contains 1 cord, because these dimensions
multiplied together are equal to 128 cubic feet.

WINE MEASUBE.

XXVII. Wine measure is used for measuring wine^ and
most liquids.

4 Gills

make

LX>JjXk.

1 Pint,

pt.

2 Pints

make

1 Quart,

qt.

4 Quarts

make

1 Gallon,

gJ.

63 Gallons

make

1 Hogshead,

hhd.

2 Hogsheads

make

1 Pipe,

pi.

2 Pipes

make

ITon.

Note. — The number of gallons which a barrel contains i»
not uniform in all the States ; some States having adopted
31)^, some 32, and in others varying from 28 to 32.

Note. — The wine gallon contains 231 cubic inches. The
imperial galloa of Great Britain contains 277.2X4; con-
sequently, it takes about 6 gallons of the former, to make 5
of the latter.

AND EAIL KOAD CALCULATOR. 21

ALE OR BEER MEASURE.

XXVni. This measure is used for measuring heer^ ale^
porter and milk.

TABLE.

2 Pints make 1 Quart, qt.

4 Quarts make 1 Gallon, gl.

36 Gallons make 1 Barrel, bl.

54 Gallons make 1 Hogshead, hhd.

Note. — A beer gallon contains 283 cubic inches.

DRY MEASURE.

XXIX. By this measure, are measured all dry wares ; as
£rain, seeds, roots, fruits^ salt, coal, sand, oysters, &c.

1 Quart, qt.

1 Peck, pk.

1 Bushel, bu.

1 Chaldron, ch.

Note. — The measure adopted by the United States is call-
ed the Winchester bushel; it is a vessel of cylindric form
18i in. in diameter, 8 in. deep, and contains 2,150^ cubic
jnches; but the imperial bushel of Great Britain, 2,218]^;
so that 32 bushels of the latter, are about equal to 33 of the
former.

Note 2. — The number of pounds adopted is not uniform
in all the States; some having adopted one number, and
some another. A standard bushel of wheat is 60 lbs., of
corn shelled 56, corn on the cob 70, rye 56, oats varying
:from 32 to 33^, salt 50, dried fruit variable.

Note 3. — A gallon of dry measure contains 26r| cubic in.

TABLE.

2 Pints

make

8 Quarts

make

4 Pecks

make

36 Bushels

make

22 THE MAN OF BUSINESS

TIME MEASURE.

XXX. This measure is used to measure the various di-
Tisions of time, whether natural or artificial.

TABLE.

60 Seconds

make

1 Minute,

min.

60 Minutes

make

1 Hour,

hr.

24 Hours

make

IDay,

da.

7 Days

make

1 Week,

wk..

4 Weeks

make

1 Month,

mo.

13 Mo., 1 da. 6 hrs.,
365 Days 6 hours

i make 1 Julian Year,

yr.

12 Calendar Months

make 1 Year,

yr.

Wote 1. — The years are numbered from the beginning or
the Christian Era. The year is divided into 12 calendaf
months numbered from January; the days are numbered
from the beginning of the month ; hours from 12 o'clock at
night to 12 at moon.

M)te 2. — The length ef the tropical year is 365 days, 5
hours, 48 minutes, 48 seconds nearly.

I^ote 3. — Since the length of the year is 365 years and 6
hours, the odd 6 hours, by accumulating for 4 years, make
a day, so that every fourth year contains 366 days. This is
called Bissextile or Leap year. The leap years are exactly
divisible by 4: 1872, 1876, 1880, are called leap years.

JVote 4. — In business transactions, 30 days are regarded
as a month.

AND KAIL ROAD CALCULATOR.

CIRCULAR MEASURE.

XXXI. This measure is used to measure latitude and
longitude, and the motions of the heavenly bodies, in their
respective orbits.

TABLE.

60 Seconds make

60 Minutes make

30 Degrees make

12 Signs or 360 deg. make

1 Minute,
1 Degree,
1 Sign,
1 Circle,

m,
deg.
s.
c.

Note. — Care should be taken not to confound minutes of
space, and minutes of times.

TABLE OP PARTICULARS.

XXXII.

12 Units or things

12 Dozen

12 Gross or 144 doz.

20 Things
100 Pounds
196 Pounds
200 Pounds

18 Inches

22 Inches, nearly

make

14 Pounds of Iron or Lead make 1 Stone.
21 J Stones make 1 Pig.

8 Pigs make 1 Pother.

1 Dozen.

1 Gross.

1 Great Gross.

1 Score.

1 Quintal of fish.

1 Barrel of flour.

1 Barrel of pork.

1 Cubit.

1 Sacred Cubic.

THE MAN OF BUSINESS

BOOKS AND PAPER.

XXXni. The terms quarto^ folio^ octavo^ decimo^ cfec, in-
dicate the number of leaves into which a sheet of paper is
folded.

TABLE.

A sheet folded in 2 leaves in called a folio.

quarto or 4 mo.

octavo or 8 mo.

12 mo.

16 mo,

18 mo.

24 mo.

32 mo.
24 sheets of paper make 1 quire.
20 quires make 1 ream.

2 reams make 1 bundle.

5 bundles make 1 ball.

' 8

' 12

' 16

* 18

' 24

* 32

PROPERTIES OP NUMBERS.

XXXiy. 1. Numbers are divided into even and odd.

2. All numbers are even which can be divided by two
without remainder; hence 24 and 8 are even numbers; be-
cause they can be divided by 2 without a remainder ; but 3,
7 and 9 are odd ; since they cannot be divided by 2 without
a remainder.

3. Numbers again are either prime or composite.

4. A number is prime when it cannot be resolved into
factors ; as 2, 3 and 5 are prime numbers ; because they can
not be divided by any number greater than one, and less
than themselves.

AND BAIL ROAD CALCULATOR. 25

5. Numbers are composite, when they can be resolved
into factors. Ex. 4, 8 and 9 are composite numbers ; be*
cause they can be resolved into factors.

6. Factors are either composite or prime ; thus 5 and 9 arc

factors of 45 ; but 9 is a composite factor ; because it can be

resolved into other factors, viz : two 3's.

Note. — Numbers whether prime or composite, are said to
be prime to each other, when they have no common factor.

FACTORINa.

l^XXV. Factoring consists in resolving a composite num-
ber into its prime factor, and depends on the following'
principles and propositions.

PRINCIPLES.

XXXVI. 1. A factor of a number, is a factor of any mul-
tiple of that number.

2. A factor of any two numbers, is also a factor of their
sum. From these principles are deduced the following

PROPOSITIONS.

I. Any number ending in 0, 2, 4, 6 or 8, is divisil)le hy 2.
By implication, no number is divisible by 2 which does

not end in 0, 2, 4, 6 or 8.

II. Any number is divisible by 4, when the number denoted
by its two right hand digits, is divisible by 4.

By implication, no number is divisible by 4, unless the
number denoted by its two right hand digits, is divisible
by 4.

III. Any number ending in 0 or 5 is divisible by 5.

26 THE MAK OF BUSINESS

By implication^ no number which does n©t end in 0 or 5,
is divisible by 5.

rv. Any nuniber ending 0, two 0'«, etc., is divisible dy 10,
100, dc.

V. Any composite number is divisible by the product of any
two or more of its prime factors.

Yi. Every prime number^ except 2 and 5, ends in 1, 3, 7 or 9.

BULES FOE FACTORING.

XXXVII. To resolve any composite number into its
prime factors.

Divide by any prime factors tJiat will divide it without re-
w^inder, and continue the operation till all the prime factors
are developed.

Ex. Resolve 84 into its prime factors.

Operation, 84-;-2=42-i-2=21-;-3=7 ; hence the prime fac-
tors are two 2's, a 3, and a 7. Proof, 2X2X3X'7=84.

Rem. 1, It is better perhaps to commence witlr. the least
prime factor.

Rem. 2. For practical purposes, it is generally sufficient
to resolve the composite numbers into factors, whether
composite or prime.

THE GREATEST COMMON DIVISOR OR MEASURE.

XXXYIII. The greatest common divisor or measure^ is the
largest number that will divide two or more numbers with-
out remainder.

RULES.

I. Resolve the given numbers into their prime factors, and, if
there is but one factor common to both or to all^ that is the great-

AND RAIL ROAD CALCULATOR. 27

est common divisor^ tut, if there are more than one common fac-
tor^ their product icill de the greatest common divisor .

Ex. Find the greatest common divisor of 35 and 49.

Operation. The prime factors of 35 are 5 and 7, and the
prime factors of 49, are two 7's, hence 7 is the only factor
common to both; it is therefore the greatest common divi-
sor.

Ex. 2. Find the greatest common divisor of 24 and 82.

Operation. The prime factors of 24 are three 2's and one
3, and the prime factors of 32, are five 2's.

Now, by comparing the prime factors of both numbers,
we find that three 2's are common to both numbers; hence
their product will be the greatest common divisor; thus,
2X3X3=8.

II. Divide the greater number hy the less and the divisor lyy
the remainder ; continue the operation till there is no remainder y
and the last divisor will de the divi^r sought.

Ex. Find the greatest common divisor of 24 and 98.

Operation. 98-:-24=4+2, 24-f-2=12.

Now, sines there is no remainder, 2 the last divisor, is

the greatest common divisor.

M)te. — If there are more than two numbers, first find the
greatest common divisor of two; secondly, find the great-
est common divisor of the divisor thus found, and another
number, and so on, till sill the numbers are exhausted, and
the last divisor will be the divisor sought.

SOLUTION OF PROBLEMS.

XXXIX. Ex. A farmer has 12 bushels of Oats, 18 bush-
els of rye, 21 bushels of corn, and 30 bushels of wheat. Re-
quired the largest boxes of uniform size, and containing an

^8 THE MAX OF BUSINESS

-€xact number of bushels into which the grain can be put,
each kind by itself, and all the boxes to be full, and also
the number of boxes necessary to contain the grain?

Ans. 38 boxes containing 3 bushels each.

Solution. Find the greatest common divisor of all the
numbers given, and this common divisor will be the size of
the box sought, (which in this case is 3) ; then divide the
sum of the given numbers by the greatest common divisor,
and the quotient will be the number of boxes sought, thus
(12+18+24+30)^3=28, number of boxes.

Ex. 2. I have 3 fields, one containing 16 acres, the sec-
'Ond 20 acres, and the third S4 acres. Required the largest
;size lots containing each an exact number of acres, into
which they can be divided, and the num])er of lots. Ans.
4 acre lots, and number of lots, 15.

THE LEAST COMMON MULTIPLE.

XL. 1. The common multiple of two or more numbers, is
a number that can be divided by each of them without a
remainder; thus 60 is a common multiple of 3, 4, and 5;
because 60 can be divided by each of them without a re-
mainder.

2. The least common multiple of two or more numbers, is
the least number that can be divided by each of them with-
out a remainder; thus 12 is the least common multiple of
3, 4, and 6 ; because it can be divided by each of them
without remainder.

3. A multiple of a number, contains all the prime factors
of that number; the common multiple of two or more num-
bers, contains all the prime factors of each of the numbers;

AKD KAIL EOAD CALCULATOR. 29

and the least common multiple of two or more numbers, con-
tains only each prime factor taken the greatest number of
times, it is found in any of the several numbers; hence the
least common multiple of two numbers, must be the least
number that will contain all the prime factors of them, and
no others.

TO FIND THE LEAST COMMON MULTIPLE.

XLI. 1. Arrange the nurnbers in a horizontal line.

2. Divide ly any prime factor that will divide two or more
of the numbers without remainder.

3. Write the quotient figures together with the undivided
numbers, under a line below, and continue the operation^ till the
quotient figures become prime or prime to each other.

4. Multiply the quotient figures and the divisor together^ and
the product will be the least common multiple.

Ex. Find the least common multiple of 5, 6 and 9.
Operation. 315-6.9

^ 5.2.3

Now, since the quotient figures have become prime, the
operation can be continued no farther ; hence we multiply
thus 3X2X5X^=90, the least common multiple. Proof. Re--
solve the least common multiple into its prime factors which
will be the same as those evolved by the analysis of the giv-
en numbers; thus 90-f-3==30-i-2=:15-i-3=:5 ; hence the prime
factors are two 3's, 2 and 5 equal to those above.

PROBLEMS FOR SOLUTION.

XLIL Three men, A, B and C, set out at the same timCj
and from the same point, to walk around the same plat of
ground; A can walk around it in 15 minutes; B in 20 min-

:30 THE MAN OF BUSINESS

utes, and C in 25 minu<"es. Ivequircd the time how long
before they come together at the point from which they set
out, and how many times each will have walked around it?

Solution. First find the least common multiple of the
numbers given, and their common multiple will be the time
required in minutes which (in this case) is 300 minutes, 300
=5 hours, and then divide the time occupied by each one
in walking around, and the quotient will express the num-
ber of times of each one respectively ; thus, 300-;-15==20,
A's number of times. 300-^20=15, B's number of times.
300-1-25=12, C's number of times.

Problem 2. A can dig 9 rods of a ditch in one day; B 12
rods, in a day; and C 16 rods: what is the smallest number
of rods that would afford exact days of labor to each work-
ing alone? In what time will each one do the whole work?
Ans. 144 rods, 16 days A's time ; 12 days B's time, and 9
days C's time.

FRACTIONS. ^

XLIII. K fraction is the expression of one or more equal
parts of a unit. Hence the unit is the foundation of all
fractions. The expresion of one of the equal parts of a
iinit, is called the fractional unit ; as, i, ^, J, &c.

TWO KINDS OP FRACTIONS, COMMON AND DECIMAL.

XLIV. A common fraction consists of two parts, one
written above the other, with a line drawn between them;
thus, i, f, &c. The relation which the two parts bear to
each other, is that of dividend and divisor^ and the line sepa-
rating them, is one of the signs of division. The figure be-

ANB EAIL BOAD CALCULATOR. 31

low the line is called the denominator; because it gives
name to the fraction, and express the equal number of parts
into which the unit has been divided, and the figure above
the line, is called the numerator; because it expresses the
number of fractional units taken into the expression. The
valtie of a fraction is the quotient of the numerator divided
by the denominator.

From the preceding definitions we deduce the following

PROPOSITIONS.

XLV. I. If the numerator de multiplied ly any number ^
the denominator remaining unchanged^ the value of the fraction
will he increased as many times as there are units in the multi-
plier.

II. If the denominator he multiplied, the numerator remain-
ing unchanged, the value of the fraction will he decreased as
many times as there are units in the multiplier.

III. ^ the numerator he divided, the denominator remaining
unchanged, the value of the fraction will he decreased.

IV. If the denominator he divided, the numerator remaining
unchanged, the value of the fraction will he increased.

V. If hoth terms of a fraction he multiplied or divided hy
the same number, the value of the fraction will not he changed.

From the principles involved in the preceding proposi-
tions, we deduce the following

RULES.

XL VI. 1. To reduce a fraction to its lowest terms, di-
mde hoth terms of the fraction hyjany number that will divide
them without remainder, and continue the operation till the)f

32 THE MAN OF BUSINESS

become prime to each other ; the fraction will then te to its low-
est terms.

Ex. Reduce 43 to its lowest terms : divide both terms of
this fraction by 7=^-^2=f .

2. To multiply a fraction by a whole number, either mul-
tiply the numerator or divide the denominator, when this can he
done without remainder.

3. To multiply a fraction by a fraction, multiply the num-
erators together for the numerator of the product, and the de-
nominators together for the denominator of the product.

Ex. Multiply % by f. Operation. |Xf=j4'^J.,

The same result will be obtained, if we divide the terms

of the multiplicand by the terms of the multiplier inverted.

Now, let us divide f by | with its terms inverted (A) ; thus,

f-^2=i ; hence the result is the same.

4. To divide a fraction by a whole number, either divide
the numerator or multiply the denominator.

5. To divide a fraction by a fraction, invert the terms of
the divisor, and proceed as in multiplication, or divide the
terms of the dividend by the terms of the divisor, when it can he
done without remainder; thus, divide I by \. Operation.

8 • 4 2

9-7-3 — t'

Note. — It will readily be perceived that, if the multiplier
is a proper fraction, the product will be less than the mul-
tiplicand, and, on the other hand, if the divisor is a proper
fraction, the quotient must be greater than the dividend.

Note. — The invertion of the terms of the divisor, is only
done as a matter of convenience ; since, as we have seen,
-the same result will be obtained, if we divide both terms of
the dividend by the corresponding terms of the diyisor;
this, however, can only be done, when the division can be
effected without a remainder.

AND KAIL EOAD OALCULATOE. 33

THE DIFFEKENT KINDS OF FRACTIONS

XL VII. 1. A fraction is proper^ when its value is less
than a unit : as, ^, f , i, &c.

2. A fraction is improper^ when its value is equal to or
greater than a unit; as, -ji -^, &c.

3. A simple fraction is a single expression; it may be
proper or improper ; as, f , ~, &c.

4. A mixed nurriber consists of an integral number, and a
fraction; as, 3f, &c.

5. A compound fraction is a fraction of a fraction united
by of or X as I of | of J, or |Xt &c.

6. A complex fraction is a fraction having a fractional

numerator or denominator or both; as,— ^, &c.

Note. — The term complex applied to fractions, is only ad-
missible as a matter of convenience ; since the relation
which the two terms bear to each other, is that of dividend
and divisor ; hence a complex expression expresses nothing-
more than the division of a fraction.

REDUCTION OP FRACTIONS.

XL VIII. 1. The reduction of fractions consists in chang-
ing their form mthout affecting their 'Golue.

1. TO REDUCE AN IMPROPER FRACTION TO A WHOLE OR MIXED

NUMBER.

1. 2 iioide the numerator ly the denominator.

Ex. Reduce ^ to a mixed number. Operation. j=3|.

34 THE MA'N OF BUSINESS

3. TO BEDUCE A MIXED NUMBER TO AN IMPEOPEB FRACTION.

Hulc. — MuUi2)Jy the whole number lyy the denominator^ and,
to the 'product^ add tlie numerator ; this amount icritten over
the denominator is the result required.

Ex. What improper fraction is equal to 3f ?

Operation, 3j=ll.

Rem. The reason of this rule is obvious; for, as one unit
has been divided into as many parts as indicated by the
denominator, all the other units muit be divided into the
same number of parts, and this is done by multiplying the
whole number by the denominator, for instance in the ex-
ample above, one unit has been divided into three parts,
and the other three expressed by the integral number di-
vided into the same number of parts, will be ^, and since
there are two fractional units expressed by the numerators,
it follows that ^+1=5^.

3. TO REDUCE A COMPOUND FRACTION TO A SIMPLE ONE.

Rule.— Multiply all the numerators together for the numera-
tor of the simple fraction, and all the denominaiors together for
the denominator.
Ex. Reduce 2 of | ot | to a simple fraction-
Operation. I of I of |=54=J.

4. TO REDUCE A COMPLEX PSACTION TO A SIMPLE FRACTION.

Rule. — Invert the terms of the denominator as direc'ed in the
division of fn c'icn.

Ex. Reduce ]4 ^° ^ simple fraction.
If

'Operation. -|= X-l-

AND KAIL ROAD CALCULATOR. 35

Wote. — This operation is proved by multiplyiug the simple
fraction by the denominator, which will give the numera-
tor, and, by dividing the numerator b}'^ the simple fraction,
it will give the denominator; thus, 9X2=18=3=1 i, again
2=1 J. (See proof of division).

4 • 9 36 3

-i~7~8 24

5. TO BEDUCE FRACTIONS OF DIFFERENT DENOMINATORS TO
A COMMON DENOMINATOR.

n. Multiply each numerator by all iJie denominators, except
its own, for the numerators required, and raultiply all the de^
nominators together for a common denominator , and then each
numerator v^riiien over the common denominator, it will he the
reduction required.

Ex. Reduce J, I, ? to a common denominator.

Operation. 1X3X5=15, 3X^X5=20, 3X2V3=18; de-
nominators, 3X3X5=30, expressed thus, ^^, |2 and ^J.

u. Divide the common denominator hy each given denomina-
tor respectively, and multiply the quotieyit hy tlie numerator ;
thus 30 being the common denominator in the preceding
example. 30-f-2=15Xl=15, 30^3=10X3=20,,. 30-^5=6
X3=18, expressed ^^ 30 and JS, the same as before.

m. Multiply both terms of the fraction by any number or
numbers that will make their denominators alike.

Ex. Reduce f and | to a common denominator.

Now, if we multiply both terms of f by 4, the result
will be il ; again, if we multiply both terms of | by 3, the
result will be /^ — the denominators are now alike. This
last method is called reduction by inspection, and often
facilities the operation. Each method may be proved by
reducing the fractions to their lowest terms.

36 THE MAN OF BUSINESS

;^ote. — The value of the fractions is not changed in any
of the preceding methods ; because both terms of the frac-
tion have been virtually multiplied by the same numbers,
(See Proposition, 5.)

TO FLND THE LEAST COMMON DENOMINATOR.

XLIX. I. Meduce all the fractions to their loicest terms.

II. Find the least common multiple of the denominators^ and
then proceed as in method second. (See least common multi-
pie.)

DECIMAL FRACTIONS. .

L. 1. A decimal fraction is a fractional expression, in

which the denominator is generally omitted, and a period

(. ), called a separatrix, is placed before the numerator.

Eem. The limits of this work will not allow us to do
more than briefly state a few of the most important princi-
ples, and rules involved in decimal operations.

2. In decimal fractions, a unit is divided into ten equal
parts called tenths ; and these again into ten other parts
called hundredths, and these again into ten other equal
parts called thousandths, and so on.

3. Decimal fractions follow the same laws of increase and
diminution as integral numbers ; hence they may be con-
veniently expressed together, and the expression is then
called a mixed number; as, 5.5, read five and five tenths.

4. The denominator consists of one and as may naughts
annexed, as there are decimal figures in the numerator.

5. The value of a decimal fraction can never equal that
of a unit, however, far extended.

6. The value of a fraction is diminished tenfold by pre-

AND KAIL ROAD CALCULATOR. 37

fixing a naught to it ; but its value is not affected by annex-
ing a naught.

7. All the operations in decimal fractions are performed
as in integral numbers, the only difficulty is in knowing,
where to place the separatrix ; this, for the most part, will
be obyiated by observing the following

RULES.

LI. I. Separate on the right hand of the product as many

decimal figures as there are in loth factors.

Ex. Multiply 5.3 by .5.

Operation. 5. SX 5=3. 65.

Note. — If there are not enough places in the product, pre-
fix naughts; thus, .05X.3=.015.

II. Sepa/rate on the right hand of the quotient as many de-
cimal figures as will equal the excess of decimal places in the
dividend.

Ex. Divide .25 by .5.

Operation. .25^.5=. 5.

m. If the decimal places in the divisor exceed those in the
dividend, annex enough ciphei^s to make them equal, and in-
this and every other case, where the number of decimal places^
are equal, the quotient will be integers.

Note. — If it is necessary to annex more ciphers to the di-
vidend, as in case of a remainder, separate as directed in
rule second ; for every cipher annexed, makes an additional
decimal in the dividend.

38 THE MAK OF BUSINESS

REDUCTION OF DECIMALS.
LII. 1. To REDUCE A DECIMAL TO A COMMON FRACTION.

Note I. — Supply the denominator, and reduce it to its lowest
terms.

Ex. Reduce .25 to a common fraction; thus, 1^=1-

ITote. — If tlie decimal is a repetend, reduce the complex
expression to the form of an improper fraction, and the
following rule will be sufficient.

Rule II. — Reduce the complex expression to tlie form of an
improper fraction, and divide by 10, 100, 1000, <&c., as the
decimals may be tenths, hundredths, thousandths, <&c., and the
quotient will be a common fraction of equal value.

Ex., first. Reduce .l| to a common fraction.

Operation. . 13==\0-^10=^.

Ex., second. Reduce .66f to a comic on fraction.

Operation. .68f-=-?^100=|.

Ex., third. Reduce .833|^ to a common fraction.

Operation. .833-5=2f-M000=-S=6-

To reduce a common fraction to decimal.

Bide III. — zinnex ciphers to the numerator^ and divide by
the denominator, and continue the operation till there is no re-
mainder, or till it become a repetend ; in this case 3 or 4 places
<we sufficient.

Ex. Reduce f to an equal decimal.
Operation. 3ooo_ 375^ Proof, ^^l.

Note. — Fractional operations are for the most part, prov-
ed as similar operations in integral numbers.

DECIMAL CURRENCY.

LIII. Dollars, cents, and mills may be called decimal
currency ; since regarding the dollar as a unit, cents ex-

AND KAIL ROAD CALCULATOR. 39

press himdreclths of dollars, and mills thousands of dollars
or tenths of cents; hence the same rules and principles ap-
ply to decimal currency as to other decimal expressions.

METALLIC CURHENCY.

LIV. The metallic currency of the United States, consists
of gold, silver and nickel coins, (the last formerly called
copper). The legal gold coins are double eagle, eagle, half-
eagle, quarter-eagle, three-dollar piece, and one dollar ; the
legal silver coins are the dollar, half-dollar, quarter-dollar,
dime, half dime and three-cent piece ; a nickel is the cent.

Note. — There are, however, in circulation fifty-dollar
piece, half-dollar piece and quarter-dollar piece, though
they are not legal ; the cent and half-cent, though still in
use, are no longer coined.

Note. — Decimal currency is only used in accounts, the
cents occupying two decimal places ; consequently, where a
less number than ten is to be expressed, a cipher is put in
place of dimes; thus, .09 equal 9 cents.

Note. — The mill has no coin corresponding to its value;
in Vjusiness transactions, no regard is paid to parts of mills,
and, when five or more go over from cents, business men
regard it as one cent ; but, if less than five, no attention is
paid to it.

DUODECIMALS.

LY. Duodecimals are a kind of denominate numbers
whose radix is 12, i.e. twelve of a lower denomination, make
one of the next higher denomination ; consequently, if we
divide a unit of a higher denomination into 12 equal parts,
one 12 vnll be equal to a unit of the next lower denomina-
tion; regarding one foot as th^ unit, if it be divided into
12 equal parts, one part will be equal to one prime or inch,

40 THE MAN OF BUSINESS

and, if we divide this into 12 other equal parts, one part
will be equal to one second ; hence one inch is one 12th of
a foot, and one second is equal to one 12th of one 12tb,
equal to il4th of a foot.

The lower denominations are distinguished by marks af-
fixed to them, called indices; thus, 1,' 2," 3,'" and so on,
is read two primes, two seconds, two thirds and so on.

Note 1. — Since the operations in duodecimals, are simi-
lar to other denominate numbers, we deem it unnecessary
to give any example.

Note 2. — Operations may frequently be facilitated by re-
ducing primes to the fraction of a foot.

Note 3. — Duodecimal fractions, as they are sometimes
called, are applicable to linear, surface and cubic measure.

ANALYSIS.

LVI. Analysis is the examination of the several parts of
a proposition or problem, and tracing the relation which
these parts bear to each other, and to the whole, and also
ascertaining the part which each element is to act or the
use which is to be made of it, in the solution.

The operation consists of a series of steps which general-
ly bear the relation to each other, of cause and effect, or
antecedents and sequence. Such a process resembles one
ascending a flight of stairs, with ^ lighted candle in his
hand; as he ascends, the light continues to fall before him,
so that the last steps will be as luminous as the first.

We generally reason from a given number to a unit, and
from that to the number required (i. e ) we ascertain what
part of the given efi'ect a single unit of the given cause, in
the shortest period of time indicated, has or can produce,

AND EAIL ROAD CALCULATOR. 41

having ascertained this fact the rest of the process comes
easy; since it is supposed that the units of some other cause,
connected with the preceding one, are equally potent.

Ex. If 3 men, in 5 days, can grade 45 feet of road, how
many feet can 5 men in 4 days grade? Ans. 60 feet.

Analysis. Now since 3 men can grade 45 feet, it follows
that one man, in the same time, can only grade one-third of
45 feet ; thus, 45-f-3=15, what one man can do in five days ;
by consequence, he can ©nly do, in one day, one-fifth of 15,
15-i-5=:3 feet. Now since one man, in one day, can grade
3 feet, 5 men can grade 5 times 3=15 feet, and that, in 4
days, four times 15=60.

Proof. — The correctness of such operations, may be prov-
ed by dividing each effect by its own cause, if correct, the
ratios or quotients, must be equal ; since each quotient or
quotients must express what a single unit of each cause in
the same time produces; thus, 45-;-(3X5)=3, and that
60^(5X4)— 3.

Rem. The solution of the preceding problem, involves
four steps : the first leads to what ©ne man can do in the
specified time, the second to what one man can do in one
day, the third to what 5 men can do in one day, and the
fourth to what 5 men can do in four days.

Ex. 3. If a family of 7 persons, consume one barrel of
flour in 12 days, required the quantity of flour that would
be sufficient for 43 persons in 14 days? Ans. 7.

Operation, 1^7=^^13=3^X43=^1=^X14=^^=7.

Rem. Analysis is of vast importance ; since almost any
problem may be solved by it, and since, in a great measure,
it supei cedes the necessity of remembering rules.

42 THE M4N OF BUSINESS

ABRIDGED FORMS OF OPERATIONS. — GENERAL RULES.

LVII. Rule I. — Perform tlie operation mentally wlien
practiccMe ; for the mind acts 7nore rapidly than words can lye
■uttered or figures made.

II. Perform the operation ty reading the nunibers instead

^f the common routine.

Note. — In reading numbers, only mention each partial
amount in addition, and in multiplication, only name the
right hand figure of each partial product increased by the
number carried, except the last product which should be
all expressed; thus: instead of saying 8 and 4 are 12, and
5 are 17, and 4 are 21, and 6 are 27,^ &c., read 12, 17, 21,
27, &c. Again, in the following Ex., require the product
of 4325X5. Now instead of saying 5 times 4 are 20, 5 times
2 are 10, and 2 are 12, 5 times 3 are 15, and 1 are 16, 5 times
4 are 20, and 1 is 21. read 0, 2, 6, 21.

///. Cancel like factors from the dividend aiid divisor when

obvious; since this will not change the relation of the numbers

to each other., nor effect the value of the quotievt

IV. Reduce such fractions as many occur in the operation to
their lowest terms.

V. Reduce fractions of different denominators to a common
denominator., by inspection^ when this can be done.

VI. In percentage use the unit (1) and common fraction in-
stead of the hundred ^100) and decimal fraction ; since the re-
sults mAist be the same ; but an operation by the former method.,
can be performed in a much shorter tiw.e than one by the latter.

VII. Multiply and divide by the aliquot parts of a dollar.,
instead of the decimal number., in performing operations in de-
cimal currency or in United States money.

VIII. When the multiplicand is a common fraction., and the
multiplier an integer^ divide the denominator (when it can be
done without remainder^) insteadof multiplying the numerator.

AND EAIL EOAD OALOULATOE. 43

IX. Divide each term of the fractional dividend lyy the cor-
responding terms of the divisor^ {when it can he done without
remainder^ ) instead of inverting its terms and multiplying.

Ex. Divide I by f . ^— f =!. Asrain with the terms in-
Yerted«-^3_.4_4_

Note. — If the aliquot part is a fractional unit, in multipli-
cation, divide the multiplicand by the denominator of the
fraction, and in division, multiply the dividend by the de-
nominator of the fraction. (See table of aliquot parts.)

TABLE OF ALiqUOT PARTS.

LVni. Cents equal to $.

((

1
16

((

1
10

((

16f

1
6"

18i

3
16

t '

1
5~

((

31i

5
16

33^

((

37^

{(

((

2
5~

56i

9
18

58J

((

7
12

.60

((

THE MAN OF BUSINESS

62i
66i

83J

87i

u
{(

EXAMPLES FOR PRACTICE.

LIX. Ex. 1. What ■will 150 yards of cloth come to at 25
cents a yard?

Analysis. Now since 25 cents is equal to t^ of a dollar^
the cost of one yard, there will be only ^ as many dollars
as yards; hence, 150-i-4==373^. Again, if I pay 37)^ dol-
lars for cloth at ^ of a dollar per yard, how many yards
did I buy? Now since the cost of one yard is 5^ of a dol-
lar, it follows that there must be 4 times as many yards as
dollars; hence, 37)^ multiplied by 4 equal 150 yards.
Again, if I pay 372^ dollars for 150 yards; what did it cost
per yard? Now it is obvious that the cost of one yard is
150th of 37i ; hence 37J-^150=i==.25.

JSfote. — Though, in the first operation, we divided by 4,.
the eficct is just the same as multiplying by ^, and in the
second operation, we multiply by 4, the effect is just the
same as dividing by 3^. (See note under Kule 2).

JVote 2. — It will be observed that the two last operations
prove the first.

Ex. 2. What will 330 yards of sheeting amount to at 16^

cents a yard. Operation, 330X6=^5 dollars. Proof, paid

55 dollars for sheeting at 16% cents per yard, required the

number of yards? Operation, 55-^^=330.

3. What will 64 yards of calico amount to at 12i cents a
jard?

AND EAIL ROAD CALCULATOR. 45

4. Paid 4^ dollars for lining at 8^ cents per yard, re-
<linred the number of yards bought?

6. What is the cost of 87 bushels of potatoes at 37J cents
per bushel?

6. What will 16 lbs. of candles come to at 31)^ cents per
pound?

Let other examples be supplied.

X. Cut off all useless decimals.

Note. — In business transactions decimals need not be ex-
tended beyond two places, or three at most.

XI. Students should le familiar with Arithmetical language^
mid with all the rules^ and tables used to facilitate operations.

XII. Keep the attention firmly fixed on the operation in hand.

SPECIAL BULES. — ADDITION.

LX. Add two columns at once.

Note. — ^In performing operations in this way, carry, as it
is called, one for each hundred, and not one for each ten.
The reason of this will be obvious to every thinlcing student.

Rem. This, at first, may appear to students awkward and
cumbersome ; but let them not despair ; but persevere, and
rough places will become smooth, and mountains plains.
The most expert accountants generally perform in this way.

ABRIDGED METHODS OF MULTIPLICATION. — SPECIAL RULES.

LXI. When naughts occur on the right hand of

EITHER FACTOR OR BOTH.

Rule I. — Multiply the digits together, and^ to their product,

annex all the naughts.

Ex. Multiply 240 by 30.

Operation, 24,0 .

3,0

7200

6 THE MAN OF BUSINESS

WHEN THE MULTIPLIER IS 10, 100, 1000, &C.

//. Annex all the ciphers in the multiplier to the multipli^
4}and, and this will complete the product.

IF THE MULTIPLICAND IS A DECIMAL.

III. Bemove it (is mtny places towards the left as there are
naughts in the multiplier.

Ex. .5X10=5. Now, by moving, 5 one place farther to-
ward the left, it becomes an integral number.

WHEN EITHER FACTOR IS A COMPOSITE NUMBER.

IV. Multiply "by its factors instead of the number itself.
Ex. 47X35. 35 being a composite number, we multiply^

by its factors 7 and 5; thus, 47X'7=329X5=1645.

JVote. — By strictly observirg this method much time will
be saved ; since no addition is required.

WHEN THE MULTIPLIER IS A LITTLE LESS THAN 10, 100,

1000, &C.

V. Annex to the multiplicand as many ciphers as there are
figures in the multiplier, and from the result subtract the pro-
duct of the multiplicand, by the number^he multiplier ladles of
Idng 10, 100, 1000, &c.

Ex. Multiply 4232X08.

Operation, first multiply the multiplicand by 3, the num-
ber the multiplier wants of being a hundred ; thus, 4232X2
=8464 ; second, subtract this from the multiplicand with
two ciphers annexed, 423200—8464=414836. Ans.

Note. — This operation may be proved by multiplying the
factors together in the usual way, and the final results will
be the same.

AND BAIL EOAD OALCULATOrv.

VI. Multiply two figures, of the multiplicand at once^
Ex. Let it be required to multiply 1225X6.
Operation, 1225
6

7350

New, instead of saying 6 times 5, &c., say, or rather
think, 6 times 25 is 150, and 6 times 12 are 72 and 1 is 73.

Rem. By this method the operation can be performed
more rapidly than figures can be made, and to have full
command of it, the pupils need only be thoroughly drilled
in the extended multiplication table (which see).

Note. — It will be observed that in performing operations
as directed above, that two right hand figures are set down
instead of one — in other words, carry for hundreds, thou-
sands, and none for tens.

THE EXTENDED MULTIPLICATION TABLE.

2 X13

X13

2 " 14

'■• 14

2 " 15

" 15

2 " 16

'• 16

2 " 17

u 1^

2 " 18

" 18

2 '' 19

" 19

2 " 20

" 20

5 X 13

—

X13

—

5 " 14

" 14

1 1

5 " 15

"'15

105

5 " 16

'' 16

112

5 " 17

" 17

102

119

5 " 18

" 18

108

( »

126

5 " 19

" 19

114

13S

5 " 20

100

" 20

120

1 7

14a

THE MAN OF BUSINESS

8 X 13

8
8
8
8
8
8

14
15
16
17
18
19

= 104
" 113
" 120
" 128
" 136

" 152

9 X13 = 117

8 " 20 " 160

" 14

" 15
" 16
" 17

" 18
" 19

" 126
" 135
" 144
" 153
" 162

9 " 20 " 180

10 X 13 = 130

10
10
10
10
10
10

" 15

" 16
a 17

10 " 20 " 200

140
150
160
170
180
190

11
11
11
11
11
11
11
11

X13

= 143

" 14

'* 154

" 15

" 165

" 16

" 176

u 17

" 187

" 18

" 198

" 19

" 209

" 20

" 220

12 X 13 = 156

12
12
12
12
12
12

14
15
16
17
18
19
20

168
180
192
204
216
228
240

Rem. This table might be extended to a hundred or
Bven beyond that ; but our limits will not allow us to insert
more.

Note. — The science involved in the multiplication table
is this, if we begin at the smallest product, and add the
multiplying figure to it, the amount will be the next suc-
ceeding product, and S3 on through the entire ascending
,'Series; but, if we begin at the largest product, and sub-
tract the multiplying figure from it, the difference will be
the next succeeding product, and so on through the entire
descending series, or what is called repeating the multipli-
cation table backwards.

Rem. Operations in multiplication may also be facilita-
ted by a mental process called inspection, by noting the
right hand figure (which will generally suggest the left) of
each product arising from multiplying together any two
digits, without going through the ordinary process of mul-
tiplying each figure separately.

AND RAIL ROAD CALCULATOR.

LXII. The following table exhibits the product arising
from multiplying any two of the nine digits as factors.

Factors

Pro

Factors

Pro [Factors

Pro

Factors

Pro

2x1-

_ 2

3x1-

4x1 —

- 5

2 " 2

" 4

3 " 2

((

4 " 2 "

" 10

2 " 3

" 6

3 " 3

■ i

4 " 3 "

5 •

" 15

2 " 4

" 8

3 " 4

4 " 4 "

5 «

" 20

2 " 5

" 10

3 " 5

( (

4 " 5 "

5 '

" 25

2 " 6

" 12

3 '' 6

((

4 " 6 "

5 <

" 30

2 " 7

" 14

3 " 7

( (

4 .. 7 «;

" 35

2 " 8

" 16

3 " 8

( (

4 " 8 "

" 40

2 " 9

" 18

3 " 9

( (

4 " 9 "

•36

" 45

2 " 10

" 20

3 " 10

((

4 " 10 "

" 50

2 " 11

" 22

3 " 11

' I

4 " 11 "

" 55

2 " 12

" 24

3 " 12

((

4 " 12 "

((

" 60

Factors

Pro

Factors

Pro

Factors

Pro

Factors

Pro

6x1

_ 6

7x1

8x1 —

— 9

0 " 2

" 12

7 " 2

( i

8 " 2 "

" 18

6 " 3

" 18

7 " 3

I (

8 " 3 "

" 27

6 " 4

" 24

7 " 4

8 " 4 "

" 36

(J " 5

" 30

7 " 5

i I

8 " 5 "

" 45

6 " 6

" 36

7 " 6

8 *' 6 "

" 54

6 " 7

" 42

7 " 7

8 " 7 "

" 63

«) " 8

" 48

7 " 8

8 " 8 "

" 72

13 " 9

" 54

7 " 9

( t

8 " 9 "

•• 81

6 " 10

" 60

7 " 10

( (

8 " 10 "

" 90

6 " 11

" 66

7 " 11

8 " 11 '

" yi>

6 " 12

" 72

7 " 12

I i

8 " 12 "

'* 108

Factors

Pro

Factors

Pro

Factors

Pro

10 x 1

— 10

11 X 1

12 X 1 -

_ 12

10 " 2

" 20

11 " 2

I 4

12 " 2

" 24

10 " 3

" 30

11 " 3

( (

12 " 3

" 36

10 " 4

" 40

11 " 4

((

12 " 4

" 48

10 " 5

" 50

11 " 5

12 " 5

" 60

10 " G

" 60

11 " 6

12 " 6

" 72

10 " 7

" 70

11 " 7

i i

12 " 7

" 84

10 " 8

" 80

11 " 8

12 " 8

" 96

10 " 9

" 90

11 " 9

i i

12 " 9

" 108

10 " 10

"100

11 " 10

110

12 " 10

" 120

10 «' 1]

" 110

11 " 11

i I

121

12 " 11

'< 132

10 " 12

" 120

11 " 12

132

12 " 12

" 144

ZO THE MAN OF BUSINESS

Note. — The numbers 10, 11 and 12 are added to make
tliis a common multiplication table.

ABRIDGED FORMS OF OPERATION IN DIVISION.
SPECIAL RULES.

LXIII. Rule I. Separate an equal nuoriber of nauglits on tJie

Tight of the dividend and divisor when they occur.

Ex. Divide 240 by 30.

Operation, 24,0-^3^0=8.

Note. — It is obvious that the quotient is not changed,
since separating the naughts from both terms is dividing-
both by the same number, consequently 24 will contain ^
^s many times as 240 will contain 30.

"WHEN NAUGHTS OCCUR ON THE RIGHT HAND OF THE DIVIDEND

ONLY.

II. Separate as many figures on the right hand of the divi-
dend as there are naughts on the right of the divisor, and pro-
ceed as defore.

Ex. Divide 675 by 40.
Operation, 67,5-^4,0=1 6-[-J^=;5.

Note. — If there is no remainder in the operation, the fig-
ure or figures are the true remainder; but, if there is a re-
mainder, it must be prefixed to the separated figure or
figures.

When the divisor is a composite number.

III. Divide the dividend ty one of the factors^ and the quo-
tient hy the other, and the last quotient icill he the one sought.

Ex. Let it be required to divide 568 by 18.
Ans. 31-1-10.

AND EAIL ROAD CALCULATOR. 51

Operation, 568-^6=94+4, 94+3=31-[-l, 64-1+4=10 re-
mainder.

Note 1. — If there is a remainder in the first operation,
and none in the second, it is the true remainder.

2. If there is a remainder in the second operation, and
none in the first,, the product of this remainder into the
first factor used is the true remainder.

3. If there is a remainder in both operations, the pro-
duct of the last remainder into the first divisor, plus the
first remainder, will be the true remainder. (See the opera-
tion above.)

IV. Perform tke operations hj short division, when practi-

tahle.

Note 1. — -It is generally practicable when the divisor con-
tains but two figures.

Note 2. — If the divisor is a composite number, proceed as
in rule III; but, if a prime number, proceed as if it were
12 or less.

Ex. Let it be required to divide 3823 by 17.

Operation, 17)3825

225 Ans.

Rem. No one will find any difficulty in operations simi-
lar to the preceding one, who is well acquainted with the
multiplication table extended; and, in many cases time
will be saved by dividing by the entire number, even when
composite. For abridged forms of operations in interest,
iice interest.

PEUCENTAGE.

LXIY. Percentage means by the hundred, and is applica-
ble to anything reckoned by the hundred.

Percentage may be divided into two grand divisions,
viz : percentage without time, and percentage with time.
Both these taken together embrace all of what is (Jailed the
business part of Arithmetic.

> ' J J J > > > > ) J J ) ) y i ) 3

^ ^ > ) :> •> , ' J J J > > :> ' -; ^ , > J J . J

' ^ ' 3 > ■> J ' i :> :> , ' i :> )' ' ] j ; J j

^ 5 ^ :, J 5 J i , , \ J i :i :> i :, \ ' i ) .5 j> 3

5 > ^ J -^ :> ) > ) } . ^ ) ^ J J 3 J ^ 3 ^ -J . J J J J j

52 THE MAN OF BUSINESS

LXy. Percentage without time, may be divided into two
parts, viz: 1st. "Where the per cent, is less than a hundred
(100,) and 2d. Where more than a hundred (100.)

1st. Per cent, less than a hundred (100.)

TERMS.

Basis, Bate Per Gent., Percentage, the Amount and Differ-
ence.

Note. — The amount and difference are sometimes called
the result and number.

DEFINITIONS.

1. The basis is the standard of comparison, and repre-
sents the buying price or cost of an article.

2. The rate per cent, expresses what part of the hundred
is to be taken, e. g. six per cent, is six of a hundred, or
six hundredths.

3. Percentage expresses the aggregate amount of the
part of each 100 contained in the basis as indicated
by the rate per cent.

4. The amount consists of the bnsis-\-i\iQ percentage, and
represents the selling price when there is a gain.

5. The difference consists of the bans — the percentage,
and represents the selling price when there is a loss.

Note 1. — The basis as the standard of comparison, is
regarded as being 100 per cent.

Note 2. — Any two of the above terms being given, the
third can be found.

AND RAIL EOAD CALCULATOR. 53

THE BASIS AND RATE PER CENT. BEING GIVEN TO FIND THE

PERCENTAGE.

LXVI. What is the percentage of 25 dollars, rate per
cent. 20 ? Ans. $5.

Analysis. Now since the rate per cent, expresses the part
to be taken of 100, 20 must be taken as many times as there
are hundred in ths basis ; then 20 must be taken 25 times,
since each dollar is equal to 100 cents; thus, 25X30=5.00;
hence the foUwing:

Rule I. — Multiply the iasis fyy the rate per cent.^ and cut off
according to the rules of decimals.

Ex. What is the percentage of $500 at 25 per cent. ?

Operation, 500X25=:$125.

Proof. Divide the percentage by the basis, and the
quotient will be the rate per cent. ; thus, $125-;-$500==25
rate per cent.

Note 1. — The reason of this is, the per centage is the pro-
duct of the basis multiplied by the rate per cent., and, if
we divide the product by one of the factors, the quotient
iQUst be the other.

Note'^. — When the per cent, is an aliquot part of 100, the
operations may be very much abridged by dividing the
basis by the denominator of the fraction which, in effect,
is multiplication ; thus, 25==i, 500Xi=125. (See table
of aliquot parts.)

Rem. In all such operations, the aliquot part of 100 will
be used instead of the decimal expression, when practi-
<;able.

EXAMPLES FOR PRACTICE.

1. What is the income of a house and lot worth $23215,
rented at 15 per cent ?
Ans. $348.75.

54 THE MAX OF BUSINESS

2. In an orchard containing 930 trees, 20 per cent, of
tbem being pear trees, how many pear trees are there?

Ans. 186.

3. The ornamental work of a certain edifice, worth
$3325, was 161 per cent, of the whole cost; what is the
cost of the ornamental work?

Ans. $554,161.

THE RATE PER CENT. AND PEECENTAGE BEING GIVEN TO
FIND THE BASIS.

LXYII. Ex. A certain traveler paid his hotel bill with
$1.75, which was 5 per cent, of all the money he had; how
much did he have?

Ans. $35.00.

Analysis. Now, since the percentage is the product

arising by multiplying the basis by the rate per cent., it

folows, as the per cent, is one factor, that if we divide the

percentage by the rate percent., the quotient will be the

basis ; thus, $1.75-^5=35 dollars; hence we have

Rule II. — Make the decimal places in the dividend and divi-
sor equal^ and divide the percentage hj the rate per cent., and,
the quotient loill l>e the hasis.

Ex. A certain drover sold 200 head of hogs, which was

20 per cent, of his entire drove ; how many did he have ?

Operation, 200-^^=1000 hogs.

Wote. — As the rate per cent, always contains two decimal
places, if there are no decimal places in the percentage
two naughts must be ai . oxed to make the decimal places
equal; the quotient will then be whole numbers; but, if
"the rate per cent, is an aliquot part of a hundred, nO'
naughts need be annexed; as in the example above.

Proof. Find the per centage on the basis by rule I., and

AND RAIL ROAD CALCULATOR. 55

if the work is correct, it will be equal to the given per-
centage; thus, 1000+. 20=200.

EXAMPLES TO BE SOLVED.

1. A merchant paid out 850 dollars for groceries, which
was 25 per cent, of his capital ; what was his capital ?

Ans. $3400.

2. A's annual income is $300, his rate per cent, being.
15. His capital required ?

Ans. 32000.

3. A certahi farmer sold 225 acres of land which was
40 per cent, of his plantation ; how many acres did he still
own?

Ans. 3872 acres.

THE BASIS AND PERCENTAGE GIVEN TO FIND THE RATE

PER CENT.

LXVIII. Ex. A. receives $300 from a capital of $1200 ;;
what is the rate per cent. ?

Analysis. Now, since $1200 produces $800, it follows

that $1 will produce one 1200th part of 300; thus, SOO-f-.

1200=j-J-J-o=i=25 per cent. ; hence we have the following

Hide HI. — Divide the percentage hi/ tJie dasis, and tlie quo-
tient reduced to a decimal will he the rate per cent.

Ex. If the basis be 225, and the percentage 45; what is,
the rate per cent. ?

Operation, 45-^225=.£==^=20 per cent.

2. A farmer owned 525 acres of land, he sold 320 acres ;
what per cent of the whole does he still own?

Ans. SOg'j per cent.

56 THE MAX OF BUSINESS

3. John bouglit a knife for .75, sold it and made 15 cts.
by the trade; what per cent, did he make?
Ans. 20 per cent.

BASIS AND RATE PER CENT. GIVEN TO FIND THE AMOUNT.

LXIX. Ex. If I pay $5 for a yard of broad cloth; what
must I sell it for to make 20 per cent. ?

Analysis. Since multiplying the basis by the rate per ct.,
will produce the percentage, and multiplying any number
by a unit, the product will be equal to that number ; it fol-
lows that, if we multiply the basis by the rate per cent. -|- a
unit (1), the product will be the amount ; thus, 20 per cent.
==l ©f a dollar -f 1==^X$5=$6, the amount, hence we have
the following.

Bule IV. — Multiply the hasis dy the rate pe?' cent, -f 1, the
product will ie the amount.

Ex. If I buy calico at .10 per yard^ what must I sell it

for per yard to make 25 per cent. ?

Solution. (i+l)==fX10=4o=122- cents, the amount.

Note. — The operation may be performed decimally with
the same result, by using 100 instead of 1.
Thus, . 25+100=1. 25X10=.125=.12| cents.

THE BASIS AND RATE PER CENT. GIVEN TO FIND THE DIF-
FERENCE.

LXX. Note. — The operation is performed precisely as in
article LXIX, except the rate per cent, subtracted instead of
added; hence we have the following,

Rule V. — Multiply the basis by 1 minus the rate per cent.^
and the product will be the difference.

AND RAIL ROAD CALCULATOR. 57

Ex. If I pay $5 for an article ; what must I sell it for,

losing 20 per cent. ?

Solution. l=l—l=lX$5=U-

Rem. It will be easily perceived that 5 bears the same re-
lation to 1, that 20 does to 100.

2. Bought a horse for $80, but finding his qualities not
good, am willing to lose 16fper cent. ; for what must I sell
him?

3. Ans. $66.66f cents.

3. Bought broad cloth for $3 per yard ; finding it to be
damaged, I am willing to lose 12^ per cent. ; the selling
price required?

Ans. $2.62^.

KNOWING THE AMOUNT AND RATE PEE CENT. TO FIND THE

BASIS.

LXXT. Wote. — ISTow since the amount consists of the
"basis -f the percentage, it follows that the basis must con-
sist of the amount minus the percentage of the basis, con-
sequently, if we divide the amount by the rate per cent. +
a unit (1), the quotient will be the basis ; hence we have
the following.

Bule VI. — Divide the amount hy '[ -\- tlie rate 'per cent, or
deciTnally 5y 100 + tt^^ rate per cent.., and the quotient will he
the hasis.

Ex. If I sell a cow for $32, and make 33 J per cent. ; what

did she cost me? Ans. $24.

Operation, $32-1-3=24 dollars.

Rem. It will be observed that rule VI, is the converse of
•rule IV, and that they mutually prove each other.

58 THE MA'N OF BUSINESS

2. Having paid 24 dollars for a cow, what must I sell her
for to make 33^ per cent. ? Ans. $32.

3. Having paid 377 dollars for house rent, it being 16
per cent, more than I paid last year ; required the rent f er
last year! Ans. 325 dollars.

4. If a merchant sell calico at 12^ cents per yard, and
makes 12 J per cent. ; what did it cost per yard? Ans. Hi
cents.

DIFFEKENCE AND RATE PEK CEI^T. GIYEN TO FIND THE BASIS.

LXXII. J^oie. — The difference, as we have seen, consists
of the basis — the percentage; it follows, therefore, that
the basis must consist of the difference, plus the percent-
age of the basis; hence we have the following.

Hule VII.— Divide the difference hj the unit (1) — the rate;
the quotient icill he the iasis.

Ex. If a merchant sell molasses at 372^ cents per gallon,
losing 6 J per cent. ; required the cost per gallon? Ans. 40
cents.

Operation, 37^-1-1 — 1\=40 cents.

Proof, 40— 37i=2|^40=-,\ of a dollar=6i cents.

Rem. Rule VII is the converse of rule Y, and may be
proved by it.

2. Sold a horse for $80 per cent., and lost 8^ per cent. ;
required the cost? Ans. $87.27f,.

THE BASIS AND SESULTANT NUMBER GIVEN TO FIND THE
RA'. '. PER CENT.

LXXIII. Ex. If I pay $75 for a horse, and sell him for
100; what per cent, do I make?

Analysis. Now since I sold the horse for $100 for which

AND EAIL ROAD CALOULATOK. 5^

I paid $75, it follows that 100—75=^25 the sum made; now
since I made $525 on $75. I can only make one 75th of 25
on one dollar; thus 25-:-75=^'J--=i-=33i per cent. ; hence we
have. ^

Buh VIII. — Divide the difference deUoeen the dasis and the
resultant number hy the basis, and the quotient reduced to a de-
cimal will be the rate per cent.

Ex. If I pay $100 for a horse, and sell him for $75 ; what
per cent, do I lose? Ans. 25 per cent.

Operation, 100— 75=25-^100=/o^o=i=25 per cent.

EXAMPLES FOR SOLUTION.

LXXIV. If I pay 11 cents per yard for calico, and sell
it for 12 J cents per yard; what per cent do I make? Ans.
13n per cent.

2. Bought sheeting at 14 cents per yard, and sold it at
1C|- ; required the rate per cent. ? Ans. 19 J per cent.

Proof by rules IV and V.

Ex. 1. If I sell cloth at 25 cents per yard, which c©st 3Gf
cents; what per cent, do I lose? Ans. 16f per cent.

2. Bought cotton for 20 cents per pound, sold it for 22^
cents; what per cent, did I make? Ans. 12} per cent.

3. A boy bought an orange for 5 cents, and sold it for 6^
cents; what per cent, did he make? Ans. 25 per cent.

TO FIND WHAT PEE CENT. A GIVEN NUMBER IS OF ANOTHER
GIVEN NUMBER,

LXXY. Ex. What per cent, is 2 of 5?

Analysis. The number proposed as the per cent, of an-
other sustains the relation to that number as the percentage
to the basis ; thus, 2^5=5=40 per cent. (See rule III.)

€0 THE ma:n^ of business

PROBLEMS.

1. "What per cent, is 9 of 27? Aus. 33 J per cent.

2. What per cent, is i of 5 ? Ans. 621 per cent.

FORMULAS OF PERCENTAGE.

LXXYI. 1. The percentage = the dasis X ^^^ rate.

2. The lasis = to the percentage -^ the rate.

3. The rate = percentage -^ hase.

4. The amount = the iasis X <^ "^^^^ (1) + ^^^ ^^^^•

5. 17ie difference == the lasts X <^ '^^^^^ (1) — ^^^ ^^^^•

6. The dasis = i^^e amount -i- a 'wwi^ + ^A*? rate.

7. TAd 5a«i's = difference -^ a unit (1) — the rate.

8. TAe rate per cent. =the difference between the base and
resultant number ~ the base.

MISCELLANEOUS EXAMPLES.

1. In a certain battle, 78 men were killed, which was 13j
per cent, of all engaged; required the number engaged?
Ans. 585 men.

2. If I sel]^^ of an article for as much as I paid for f of
it; what per cent, did I make? Ans. 14, per cent.

RATE PER CENT. ABOVE 100.

LXXVII. I^ote. — The basis being the standard of com-
parison is neither more not less than 100 per cent.

Now since multiplying by a unit (I) the product is equal
to the multiplicand ; then, if we multiply the basis by (1),
the product will be equal to 100 per cent., and, if by 2 the
product will be 200 per cent ; hence we have the following.

AND RAIL EOAD CALCULATOR. 61

THE BASIS AND BATE PERCENT. GIVEN TO FIND PERCENTAGE.

Rule I.— Add a unit for every additional liundred^ and
multiply the lasis hy the amount, and the product wilfbe the
percentage.

Ex. Find the percentage of $25 at 200 per cent.

Operation, $25X3=150, the percentage.

Note — If the per cent is more than 100 and less than 200,
or more than 200 and less than 300, reduce the part of a lOO*
to a fraction, and add it to a unit or units as the case may
be, and multiply as before.

Ex. What is the percentage of $25 at 150 per cent?

Operation, 50==14-1— UX$35=$37i

THE BASIS AND RATE PER CENT. BEING GIVEN TO FIND THE

AMOUNT.

LXXyill. Ex. If I pay $15 for an article, what must I
sell it for to make 200 per cent. ?

Analysis. Now since multiplying the basis by 1, the pro-
duct will be the basis and, if we multiply the basis by 2 the
product will be the per centage; consequently, if we nml-
tiply by l-[-2=3, the product must be the amount; tlms,
$15X$3=|15, the amount; hence we have.

Rule IT. — Adda unit for each hundred, and muMply the
hasis l)y the sum thus found., and the product will he the amount,

Ex. If I pay $32 for an article ; what must I sell it for,

to make 300 per cent ?

Operation, 1+3=4X32=$128, the amount.

THE AMOUNT AND RATE PER CENT. GIVEN TO FIND THE BASIS.

LXXIX. Ex. If I sell a horse for $125, and make 100
per cent., what did he cost me?

62 THE MAX OF BUSINESS

Analysis. As the amount consists of the basis + the per-
centage ; it follows that, if Ave divide the amount by a unit,
-[- a unit, the quotient must be the basis; thus, l-)-l=2;
fl25-^2=$62.50; hence we have.

Bule III. — Divide the amount hy a unit -\- a unit or frac-
tions of units representing the rate per ceni.^ and the quotient
will le the hasis.

Ex. If I sell an article for $250, and make 125 per cent ;
what did it cost me? Ans. ^111 9.

2. What is the percentage on 3 of a dollar, at 200 per
cent.? Ans. $1.

3. What is the amount of %\, at 175 per cent.? Ans. %\\.

4. If I sell an article for 5 of a dollar, and make 115 J per
cent. ; what did it cost me? Ans. g^.

Note. — When there is a loss, percentage never can exceed
100 percent. ; since it is impossible to lose more than all;
but, when there is a gain, it may exceed 100 ; because more
than 100 per cent, can be made on a 100 (the basis being re-
garded as 100 per cent.,) it may be doubled, trebled, and
quadrupled, &c.

Rem. Percentage has a very extensive application in
mercantile transactions, and also in the ordinary business
of life,

PARTNERSHIP OE COMPANY BUSINESS.

LXXX. 1. Partnership is as an association of two or
more in business with an agreement to share the profits or
losses, proportionate to each one's share or stock.

2. The persons thus united are called partners.

3. The money, property or labor invested in trade is call-
ed capital or stoch^ and the amount v/hich each one contri-
butes is called his share.

AND EAIL EOAD CALCULATOR. 6'6

4. Profit is the increase of capital between two given
dates.

5. Lossi^ the decrease of capital between two given dates.

6. The amount apportioned to each partner is called
dividend.

7. The assets of a firm are its cash on hand, property and
all debts due to it.

8. The liabilities of a firm embrace all the debts which it
owes, and all its endorsements.

9. The firm is solvent w^hen its assets exceed its liabilities,
and insolvent when its liabilities exceed the cash value of
its assets.

10. When the capital is employed for an equal length of
time or when no time is specified, it is sometimes called
simple partnership ; but, when the periods of time are un-
equal, it is generally called compound partnership.

Note. — It will readily be perceived that the capital or
^tock corresponds to the basis in percentage, and the gain
or loss to percentage, and that each partner's share is a
partial basis ; hence we have the following.

liule I. — Divide the gain or loss by the capital, and multiply
each partner'' s share by the quotient^ and the product ivill be
each partner'' s share of the gain or loss, respectively. (See rules
I and III in per centage.)

Ex. A and B entered into partnership : A contributed
-1180 and B, $140; they gained $80. What is the gain of
each?

Operation, $18O+$140=32O. $80^320= 3M=i.

Again, 180Xi=45, A's share; 140Xi=35, B's share.

Proof, 45+35=80.

Note. — It will be observed that the loss or gain divided
by the capital is tlie rate per cent. ; consequently, by mul-

<y4: THE MAN OF BUSINESS

tiplying eacli partner's capital, the product will be the per-
centage respectively, and that the sum of these several pro-
ducts, is equal to the given gain or loss, if correct, and
that this result is the proof of every operation.

Mte 2. — The same result will follow, if we find each
partner's fractional part of making such share the numera-
tor of the fraction, and the entire capital the denominator,
and multiply each one's part by the gain or loss.

Ex. A, B and C entered into partnership. A contributed
^200, B, $300 and C, $400. By the operation, they made
$150. Required each one's share of the gain?

Operation, 200+300+400=900, the entire capital. 200+
900=^, A's part at the capital. 300-+900==B's part. 400+-
900=J=C's part. Again 9^X150=33^, A's share. ^X150=
50, B's share. lX^bO=Q6^, C's share. Proof, 33J+50+
661=150.

PARTNERSHIP WITH UNEQUAL TIME.

LXXXI. Note. — When capital is invested for different
periods of time, the gain or loss is not only proportionate
to the amount of capital contributed; but, also to the time
it is continued in trade; hence, to find each partner's gain
or loss, we have the following.

Rule IL — Multiply each partner's capital hy the time U is
continued in trade, and then proceed as in rule I.

Ex. A and B formed partnership : A put in $80 for S
months, and B, $40 for 5 months. By the operation they
lost $50. Required the loss of account?

Operation, 80X3=240; 40X5=200; 240+200=440, en-
lire capital. 50+440=/,X240=27,/i, A's share, 1^X200=
22^^. Proof, 27fi+228=50.

AND BAIL EOAD CALCULATOR. 65

PROBLEMS.

1. A and B agree to raise a cotton crop jointly, which
they are to divide as follows: B is to take li lbs. as often,
as A takes li lbs. ; what part of the crop should each one
elaim, suppose they raise 7,000 lbs., what will be the share
Hof each? Ans. A's part f ; B's, ^; A, share of crop, 3,000
lbs. B's, 4,000 lbs. As the solution of problems like the
above is somewhat peculiar, a brief explanation is perhaps

35 • j_

needed. The sum of the two parts, viz: li+l|=-i2, is to
be regarded as the basis, but each part taken separately is
the percentage, and the quotient of each part divided by
the sum of the parts as the rate per cent. Thus 1^4-11=
35. ii_i-3i_3 A's: !—3A's=* B's part.

2. C and D together raised a tobacco crop=4, 200; they
agreed to divide it as follows, every time C took f of a pound,
D took li pounds. What is each one's part, and what share
«f the crop should each one claim? Ans. C's |, D's |, C's
1,680 pounds, D's 2,520 lbs.

3. One of the stockholders of a rail road company owns
18 shares of $50 each ; the dividend is declared to be 7i per
cent, premium; what ought he to receive? Ans. $67.50.

BANKRUPTCY OR INSOLVENCY.

LXXXn. Bankruptcy refers^to business failure, and in-
ability to meet pecuniary liabilities.

2. A bankrupt is one who fails or becomes unable to pay
his debts.

3. An assignee is a person selected to take charge of the

66 THE MAN OF BUSINESS

property, and effects of a bankrupt, to convert the same

into cash, and after deducting the necessary expenses of

settling, to divide the net proceeds as the law requires

among the creditors.

Note. — The net proceeds of a bankrupt estate, is the dif-
ference between the available assets, and the necessary ex-
penses of settling the estate; hence, for the solution of
problems in bankruptcy we have the following.

Rule. — Divide the net proceeds by the amount of indehted-
Tiess, and the quotient will be the rate per cent, on each dollar ;
then each man's claim being multiplied by the rate per ce^it,, will
yield each dividend respectively.

Ex. A, B & Co. have failed. Their indebtedness, $3,000 ;
their assets at cash value $1,500; the expenses of settling,
$500 ; what can they pay on the dollar ; and what will D re-
ceive whose claim is 700 dollars? Ans. 50 per cent. D will
receive $350.

Operation, 1,500— 500=1, 000-1-2, 000=^=50 per cent.
S700X50 per cent. =350, D's dividend.

2. C, S & Co. having failed in business, their liabilities
are $63,500; their assets have a cash value $52,384; the ex-
penses of settling $1,584, how much can they pay on the
dollar, and what dividend should J. D. receive whose claim
is $8,361.55. Ans. 80 per cent. J. D. received $8,689.24.

ASSESSING TAXES.

LXXXIII. A tax is a sum of money assessed by the gov-
ernment on individuals, corporations, societies, districts, &c.

2. Taxes for government purposes are imposed on prop-
erty and in most states on persons.

3^ The tax imposed on persons is called poll or capita-
tion t«rX.

AND KAIL ROAD OALCULATOE. G7

4. Immovable property, such as lands, houses, mills, &c,,
is real estate.

5. All movable property of whatever kind is called per-
sonal property.

6. In assessing taxes, the first thing to be done is, to take
an inventory of all taxable property together with a com-
plete list of all the polls.

7. 'The amount of taxes, assessed on any state, town or
corporation, diminished by the capitation tax, is the per-
centage of all the taxable property ; consequently, the value
of the taxable property is the basis, and the quotient of the
percentage, divided by the basis is the rate per cent. ; then
the value of each man's property multiplied by the rate, -[-
Ms poll tax, if any, will be his tax ; hence we have the fol-
lowing

Rule. — Subtract the poll tax from the a'inount to be raised,
divide the remainder by the a'mount of taxable property by the
rate per cent. , thus found., to which add his poll tax, if any,,
€ind. the result will be the tax sought.

Ex. A tax of six hundred dollars, is to be levied on a cer-
tain town whose taxable property is valued at Si 00, 000 ; there

being 80 polls at $1.25 per poll; required A's tax, who owns
^600 worth of taxable property, and pays one poll.

Operation, 80X^1. 25==$100; $800— 100=$500-M100,OOa
=.005 (5 mills). 800X5 mi.=$44-1.25==$5.25 A's tax.

2. A certain town is to be taxed $4,280; the property on
which the tax is to be levied, is valued at $1,000,000; there
are 200 polls each taxed $1.40 ; the property of B, is valued
at $2,800, and he pays 4 polls; what will be the tax on each
dollar, and what will be B's tax? Ans. 4 mills on the dol-
lar; B'stax, $16.80.

68 THE MAN OF BUSINESS

Note. — These and similar operations may be proved by-
subtracting the capitation tax, if any, from the tax of any
individual ; divide the tax thus found by the number rep-
resenting the value of his taxable property which will give
the per cent, on the dollar — by this per cent, multiply the
number representing all the taxable property, and the pro-
duct wall be equal to the amount to be raised on the taxable
property of any given town, corporation, or state.

Note 2. — When a tax is levied on personal property, it
must be added to that levied on real estate.

COMMISSION, BROKERAGE AND STOCKS.

LXXXIV. Operations, in commission and brokerage, arc
substantially the same ; the only difference is the former is
on a larger scale than the latter, and as rules have already
been given in percentage which apply to every case, they
need not be repeated here.

COMMISSION.

LXXXV. Commission is an allowance made to an agent
for the purchase or sale or care of property.

2. This agent is called a factor or correspondent or com-
mission merchant.

3. Commissions are estimated at so much per cent, on the
money employed.

4. The goods sent, are called a consignment, the person

who sends them a consignor, and the person to whom they

are sent, is sometimes called a consignee.

Note. — Since the rate per cent, is not fixed bylaw, it var-
ies very much in different places ; but that charged on real
estate is generally mucli^ess than that on goods.

AND EAIL KOAD CALCULATOR. 69

BROKERAGE.

LXXXVI. Broherage is merely the commission paid to a
broker or dealer in stocks, money or bills of exchange for
transacting business.

STOCKS.

LXXXYII. Stocks are government funds, stock bonds,
the capital of banks, insurance, railroad, and manufactur-
ing companies, &c.

2. This capital or money paid in, is divided into shares
which are owned by stockholders.

3. The original cost of a share is its par value.

4. If it sell in the market for more than its original .cost,
it is said to be above par or at an advance ; if it sell for less,
it is below par or at a discount.

5. The original cost of a share is usually 100 dollars,
though it is sometimes $25, $50, $500, &c.

6. The rise or fall in stocks is a per cent, on the par value.
Thus a share whose par value is ^ at 16 per cent, advance,
will bring '^-^^ of its original cost; at 16 per cent, discount,
will bring ^^ of its original cost.

7. The profits of thcbc companies are every year or every
half year, divided among the stockholders.

8. The amount so paid out is called a dividend.

MISCELLANEOUS EXAMPLES.

LXXXVTII. An agent having sold $6,000 worth of goods,
his commission being 8j per cent. ; what amount must he
remit to his consignor? Ans. $5,500.

70 THE MAN OF BUSINESS

2. If a commission merchant sell $6,000 worth of goods
at 8^ per cent. ; how much ought he to receive for the sale?

Ans. $500.

3. A consignee has received $500 for the sale of goods,
his commission being 8^ per cent. ; what amount of goods
did he sell? Ans. $6,000.

4. A factor sells 60 bales of cotton at $425 per bale, and
is to receive 2i per cent, commission ; how much must he
pay over to his principal? Ans. 24,862 50.

5. I collect for A $268.40, and have 5 per cent, commis-
sion; how much do I pay over? Ans. $254.98.

6. G sends $28,638.50, to his broker, to be invested in
bank stocks which are 12|^ per cent, above par, for which
Ills broker is to receive i of 1 per cent, commission ; how
many shares of $127 can he pay? Ans. 200 shares.

Solution. 12^+i=12f +100=1121; $28,638.50+1121==
25,400+127=200 shares.

INSURANCE.

LXXXIX. Insurance is a contract by which an indivi-
dual or company binds themselves to make good any loss,
damage of property by fire or storms at sea or other casual-
ties.

2. Ships and their cargoes, houses, furniture, cattle, &c.,
are insured.

3. Life insurance is a guaranty for the payment of a cer-
tain sum of money on the death of the insured.

4. Health insurance secures a weekly allowance during the
sickness of the insured.

5. This assurance is affected in consideration of a sum of

AND RAIL ROAD OALCULATOE. 71

money, called a premium, which is paid before hand,, to the
insurers or underwriters.

6. This written agreement of indemnity, is called a policy.

1. The premium is estimated at a certain rate per cent. .
on the amount insured.

Ex. Mr. Russell paid $2,800 for his house and its insur-
ance ; insurance being 5 pesr cent. ; what did the house itself
cost him and what did he pay for the insurance? Ans.
$2,666.66f cost of house. $133. 33^ insurance.

Solution. 5 per cent.=i +g=|, ; ^3,8O0-^|J=$2,666.66§ ;
$2, 800—2, 666. 66f =$133. 33^.

2. A insured his house and stock of goods at $5,000; the
rate being 3 per cent. ; required the insurance money?
Ans. $150.

3. An insurance of $12,000 was affected on a ship at sea
at a premium of 2 per cent. ; what did the premium
amount to?

PROFIT AND LOSS.

XC. The process of estimating the gains and losses in
trade is called prq/lt and loss.

2. The gain or loss in trade is either the increase or de-
crease of the basis; since calculations generally proceed
from it.

3. Now since the cost of an article is the basis, and the
gain or loss the percentage, it follows that the rules which
have already been given in percentage, apply equally well
to all operations in profit and loss, it therefore supercedes,
the necessity of their repetition here. (See rules 4 and 5^
9 and 7.)

72 THE mk.-N OF BUSI]N^EgS

A grocer purchased a quantity of molasses for which he
paid 32 cents per gallon ; what must he sell it for per gal-
lon to make 33 J per cent.? Ans. 43t.

A merchant bought a quantity of broad cloth at $4 per
yard, but finding it some what damaged, he is willing to
lose 8 J per cent. ; the selling piice required? Ans. $3.33j.

EXCHANGE.

XCI. Exchange is the method of transmitting money

from one place to another by means of bills of exchange.

JVote. — When the places designated are in different coun-
tries, it is called foreign exchange ; but if they are in the
same country, it is called domestic or inland exchange. The
limits of this work will not allow us to do more than to
state a few plain facts involved in the latter.

2. Bills of exchange also called drafts or checks, are
written orders for the payment of money.

3. A sight hill is one payable at sight.

4. A time Mil is payable at a specified time after sight
or date.

5. The signer of the bill is the maker or drawer.

6. The one to whom the draft is addressed, and who is
requested to pay it, is the drawee.

7. The one to whom the money is ordered to be paid is
the 'payee.

8. The one who has possession of the draft is called the
owner or holder. When he sells it, and becomes an endorser,
he is liable for payment.

9. A special endorsement is an order to pay the draft,
to a particular person named, who is called endorsee^ and
no one but the endorsee can collect the bill. When the

AND RAIL KOAD CALCULATOR. 73

«ndoTsement is a blank, the payee merely writes his name
on the back, and any one who has lawful possession of the
draft can collect it.

10. If the drawee promises to pay at maturity, he writes
across the isbce the word accepted, with the date, and signs his
name; thus: "Accepted February 10th, 1873. H. Hint on. '^

11. The acceptor is first responsible for payment, and the
draft is called an acceptance.

12. A bill of exchange, like a promissory note, may be
payable to order or dearer, and it is subject to protest in
case the payment or acceptance is refused. It is generally
subject to 3 days of grace, whether a sight or time bill.

THE FORM OF AE INLAND DRAFT.

XCIL $1500. Raleigh, Feb. 10, 1873.

Please pay at sight W. and D. , or bearer, fifteen hundred
dollars, value received, and charged.

To K. and C, Brokers in . T. A.

Note. — The face of the bill being regarded as the basis
or standard of comparison, the exchange will be at par, a
premium, or discount ; hence we have the following general
rule:

Represent the face of the till at 100 per cent., and then pro-
ceed according to rules already ginen in percentage, as the na-
ture of the case may require.

BARTER.

XCIII. Bart&r is an exchange of commodities — such, for
instance, as exchanging grain, butter, eggs, chickens, and
other agricultural products, for dry-goods, groceries, &c.

74 THE MAN OF BUSINESS

GENERAL RULE OF OPERATIOBT .

XCIV. Find the amount of the commodity to he exchanged^
at the given pi'ice, and then divide the amount ty a number
representing the price of a concrete unit of the commodity to de
exchanged, and the quotient will he the number of yards^ pounds^
gallons, &c., sought.

Ex. How many yards of calico at 14 cents per yard
should a lady receive for 22 pounds of butter at 20 cents
per pound. Ans. 81?.

Operation, 22X. 20=4.40-^14=37^.

Proof. Estimate the number of yards thus found by the
given price, and the result will be equal to the former ;
thus, 31^ yards at 14 cents per yard=$4.40.

2. How many gallons of molasses at 40 cents per gallon
«hould a farmer receive in exchange for 32 busheli of oats
at 62^ cents per bushels? Ans. 50 gallons.

8. How many yards of cassimere at $1.30 per yard
should be given in exchange for 9 bushels wheat at $3 per
bushel? Ans. 13 yds. 3 qrs. 1^ na.

4. How many pourds of sugar at 15 cents per pound
should I receive for 12 dozen of eggs at 18 cents per
dozen?

5. How many yards of broadcloth at $4 per yard ought
I to receive in exchange for 24 bushels of rye at 80 cents
per bushel?

6. How many yards of sheeting should be given in ex-
change for 25 pounds of feathers at 45 cents for pound?

Note. — Questions which have no answers annexed, should
1)G proved.

AND RAIL ROAD CALCULATOR. 75

CUSTOM HOUSE BUSINESS.

XCV. Duties or customs are the toll, tribute, tariff or
taxes payable upon merchandise exported and imported.

3. These duties or customs, established by Congress and
collected by custom-house officers at various ports of entry,
constitute a part of the revenue of a country.

3. Duties are either specific or ad xalorera.

4. A specific duty is a fixed sum on a ton, hundred weighty
hogshead, gallon, yard, &c., without regard to the value
of the commodity.

5. An ad valorem duty is a percentage on the cost of
the article in the country from which it is imported.

6. Gross weight i^ the entire weight of merchandise with
the cask, barrel, bag, &c., containing it.

7. Net iceigJit is the weight of the merchandise after all
deductions.

8. Duties are computed on the net weight.

9. Lraft is an allowance for w^aste.

10. Tare is an allowance for the weight of cask, box,
&c., deducted after the draft.

11. Leakage and breakage are an allowance of 2 per
cent, for the waste of liquors in casks, paying duty by the
gallon; of 10 per cent, on beer, ale and porter in bottles,
and 5 per cent, on all other liquors in bottles. The follow-
ing is the allowance for draft :

On 112 lbs. it is

From 112 to 224 lbs. "

" 224 to 336 " "

" 336 to 1120 " "

" 1120 to 2016 " "

Above 2016 '' "

Consequently 9 lbs. is the greatest draft allowed.

lb.

lbs.

76 THE MAN OF BUSINESS

Note. — Though not mentioned in a question, dr^ft or
leakage must be deducted before the other specific allow-
ance is made.

Note 2 — In estimating ad valorem duties, no deductions
of any kind are made where there is actual tare, or actual
leakage or waste.

Note"^. — Tare is of three kinds, viz: legal tare, or such
as is established by law ; customary^ is that which is agreed
upon among merchants; actual tare, or such as is found by
actually weighing the boxes, bags, &c., that contain the
goods.

Note 4. — Questions in custom-house business, are solved
by rules already given in percentage.

Ex. What will be the duty on 225 bags of coffee, each
weighing gross 160 lbs., invoiced* at 6 cents per lb., 2 per
cent, being the legal rate of tare, 20 per cent, the duty?
Ans. $418,068.

Operation, 160 pounds — 2 lbs. ==158X325, number of bags,
35,550X6 cts.=2,]33.00X3 per ct.=$42.66; 2,133.00—42.
66=$2, 090. 34X30 per ct. ^418,068.

2. At 40 per cent, ad valorem, what will be the duty on
346 poundi of scM^ng silk, bought at Florence at $2.50 per
pound, Ans. $346.00.

3. What is the duty on 150 bags of coffee, each weigh-
ing 158 pounds, invoiced at 7 cents per pound, the tare
being 4 per cent, and duty 20 per cent. ?

4. What is the duty on 45 casks of wine, of 36 gallons
each, invoiced at $1.25 per gallon, at 40 per cent, ad
valorem?

* An invoice is a schedule of tlie articles imported, together with the
cost.

AND RAIL KOAD CALCULATOR. IT

PEECENTAGE INVOLVING TIME.

XCVI. Percentage involving time embraces interest sim-
ple and compound, true discount, bank discount, and
equation of payments.

SIMPLE INTEREST.

XCVII. Terms — Principal, Bate per cent. Interest, Time

and Amount.

Rem. — Any three of tliese being given, the fourth may
be found.

Dejinitions. — Interest is a charge made for the use of

money.

2. The principal is the sum on which the interest is
computed, and corresponds to the Ijaus in percentage with-
out time.

3. The rate 'per cent, expresses what a dollar draws in
one year.

4. The interest is the percentage expressing the aggre-
gate amount of the several parts of dollars contained in the
principal as indicated by the rate per cent.

5. The time expresses how long the principal has to run.

6. The amount consists of the principal, plus the in-
terest.

PRINCIPAL, RATE PER CENT., AND TIME GIVEN TO FIND THE.

INTEREST.

XCVIIL Ex. What is the interest of |5, at 6 per cent.,
having 8 months to run? Ans. 20 cents.

Analysis. Now, since the rate per cent, is the interest
of §1 or 100 cents for one year or 12 months, it follows

78 THE MAN OP BUSINESS

that the rate per cent, divided by 12, will express what a
dollar draws in one mouth ; thus, $6-;-12=^=i. Again
since a dollar draws 2 cent in one month, 5 dollars must
draw 5 times ^; thus, ^X5="2- Again, since 5 dollars
draw in one month, it follows that it will draw 8 times
that in 8 months; thus, |;X8=^°==20 cents, the interest; or

it may be briefly stated as follows: ^y(^i=l=J^==20 cents.

Rem. — ^From the preceding analysis, a rule may be form-
ed which will apply to every case in which the interest is
sought, except when time is expressed in days only ; hence
we have the following

Rule. — Multiply the interest of one dollar for one month Iry
the principal^ which will l)e tlie interest for one month; then
multiply this interest l>y the given time in months, and the 'pro-
duct will 5e the interest sought.

What is the interest of $24.64 at 8 percent., having 9
months to run? Ans. .11.4784.

Operation, fX34.64=16.42fX9=|1.4784. This and sim-
ilar operations may be proved by dividing the interest by
the time, and multiplying the quotient by 12, and dividing
by the rate per cent. ; thus, $1.4784X9=16.42fX12==$l.-
9762-^8=^24.64, the proof.

Rem. The reason of this operation will be given here-
after.

3. What is the interest of $20 at 10 per cent, having 1
year and 8 months to run? Ans. $53. 33 J.

Operation. -5+20=^X20 mo.='-^"=$3.33J.

3. What is the interest of $9 at 6 per cent, having 7

months and 15 days to run? Ans. 33 1 cents.

Note. — When days occur, reduce them to the fraction of
a month, and proceed as directed in the rule.

AND RAIL ROAD CALCULATOR.

Rem, In order to facilitate operations, a table exhibiting
Tvhat $1 will draw in one month, from 1 to 12 per cent, is
given below. The first column represents the rate per cent. ,
the second a common fraction of equal value, and the third
fractions in their lowest terms.

Rate.

Common fraction.

Lowest Terms

1 -

= 1

2 '

I 2 I
12

' 1

S '

' 3 '
12

« 1

{ 4 <■

' 1

i 9 i

t 3

24:

5 '

'5 <
12

< 5
12"

6 *

t 6 i

' 1

' 15 (

' . 5

« 7 c

< 7

8 '

i 8 «

' 2

9 '

' 9 I

' 3

' 10 i

' 5

12'

11 '

« 11 i

<■ 11

< 12 <
12

' 1

Note. — When the time is expressed in years only, the
operations may be sometimes facilitated by multiplying the
principal by the rate per cent., which will give the interest

80 THE MAN OF BUSINESS

for one year, and this interest multiplied by the number of
years, will give the interest sought.

Ex. Required the interest of $35.25 for 3 years, at 7 per
cent.? Ans. $7.4025.

Operation, $35.25X7 per cent.=|2.4675X3 per cent.=
$7.4025.

EXAMPLES FOE, PRACTICE.

XCIX. 1. Find the interest on $24.15 for 10 months at
6 per cent.

2. What is the interest of $2.10, having 30 months and
20 days to run, at 10 per cent?

3. Required the interest of $125 for 6 months and 10 days,
at 8 per cent. ?

4. What is the interest of $42.35, having 4 years to run,
at 6 per cent. ?

C. When the principal consists of cents only or

CENTS AND MILLS.

The operation may he performed hy reducing the cents or
cents and mills to the fraction of a dollar; and, proceeding ac-
cording to the rule already given, or hy finding the interest on
one cent for one month or one year as the case may ie, and mul-
tiplying the interest thus found hy the time.

Ex. What is the interest of 2 cents, and 5 mills equal to
Sj cents at 6 per cent., having 8 years and 4 months to run?

Solution. Now, since $1 draws h a cent in one month,
one cent will only draw ^J^ part of k\ thus 2-^100=^; if
one cent will draw ^l^, ^l cents will draw 22 times that;
4-^^i=M^L'> ^^^? if ^2 cents draw one ij in month, it wHl

AND RAIL ROAD CALCULATOR. 81

drawlOOtimes that in 100 months; l^'X100=-^=.^^=li cts.,
answer.

Briefly, thus, ^-rl00X22=^i,=^uX8 years and 4 months=
^,^=li cents.

CI. When the time is expressed in days only.

Rem. In computing interest, business men generally as-
sume 12 calendar months for a year, and 30 days for a
month ; but, as there are 7 months which have 31 days each^
and 4 months which have 30 days and one having but 28,
the interest will generally be a little too small, and possibly
sometimes a little too large ; but the error in any case will
be very slight; in consequence, of this, however, some bank-
ing corporations express the time of their bonds in days
only, and, as we are not allowed, in such cases to assume
30 days for a month, the following method has been devised.

Hule. — Find the interest for one year, and, then divide this
interest hy 365, (disregarding the odd hou7's), and the quotient
will ie the interest for one day; multiply the quotient hy the
number of days specified, and the product will Tje the interest
sought.

Ex. What is the interest of ^500 at 6 per cent., having

62 days to run? Ans. $5,095.

Operation. $500X6=$30 interest for one year; $30.00-f-

365=.08l3X63 days=$5.095.

Cn. Method op computing interest on English cur-

RENCY.

Note. — As it is sometimes expedient to calculate interest
on English currency, and as questions of this kind are gen-
erally found in most Arithmetics now in use, a short and
accurate method of calculating the interest on this cur-
rency, is desirable. Operations of this kind may be per-
formed in a way similar to that which has already been
6

82 THE MAN OF BUSINESS

given, viz : after reducing the given denominations to the
fraction of a pound.

Multiply the principal ly what one pound will draw in one
month, and this product hy the number of months, and the re-
■suU will de the intei'est sought in shillings.

Ex. Kequired th® interest on £ 30, at 6 per cent, for 5
months.

Operation [^ of a shillingX£ 30=^^=3s.> 5=15s. interest.

Eem. In the following table will be found what one
pound will draw in one month, from 1 to 12 per cent. :

TABLE.

Rate per cent.

Part of a shilling.

Lowest terms'.

2
60

((

ti .

4
60

1
15

1
12

((

6
60

7
60

((

7
60

((

8
60

9
60

((

10
60

1
6~

11
60

12
60

AND KAIL EOAD CALCULATOR. 83

Note. — By using the above table, operations in English
money will be almost as simple and easy as those in United
States currency.

EXAMPLES FOR PRACTICE.

CIL 1. What is the interest on £144 for 6 months and 20
days, at 5 per cent. ? Ans. £4.

2. Required the interest on 15s. for 2 years and 6 months,
at 6 per cent.? Ans. 2s. 3d.

3. "What is the interest on 12s. 6d. for 1 year and 3
months, at 6 per cent. ? Ans. 11 id.

CIII. Interest, Rate per cent, and time given to

FIND the principal.

Ex. 20 cents being the interest, 6 per cent, the rate, 8
months the time ; required the principal.

Analysis, 20-:-8==2i interest for 1 month, 2i=^X12=3a
cents, interest for one year ; now, since the interest of any
given principal, multiplied by the rate per cent., will give
the interest for one year, it follows that, if we divide the
interest of one year by the rate, the quotient will be the
principal ; thus, 30-;-6==$5, the principal. Hence we have
the following

Rule. — Divide the given interest hy the time in months, mul-
tiply the quotient Ijy 1 2, divide the product hy the rate per cent.
and the qvMient will he the principal.

Note — If the time is expressed in years only, multiplying-
by 12 should be dispensed with.

Note 2. — Operations, under this rule, are proved by cast-
ing the interest on the principal, which, if correct will be
equal to the given interest.

84 THE MAN OF BUSINESS

CIV. The principal, interest and rate per cent,

GIVEN to find the TIME.

Ex. Let the principal be $12, the interest 60 cents, the
rate 6 per cent. ; required the time.

Analysis. Now, since $12 has drawn 60 cents, it is evi-
dent that $1 will only draw ,'2 of 60 cents; thus, 60-f-12=5;
now, since $1 has drawn 5 cents, and that $1, at 6 per cent,
will draw ^ cent in one mo. ;it follows that as often as 5 con-
tains hy must be the time in months ; thus, 5^2==-10 months,
time sought. Hence we have the following

Rule. — Divide the interest hy the principal, and the quotient
l>y what one dollar loill draw in one mo7ith at the given rate^
and the result will de the time in months required.

Ex. The principal being S40, the interest ^1.60, and the

rate 8 per cent. What is the time? Ans. 6 months.

Operation, $1.60-^-40=4 cents; 4-^1=6 months.

CV. The principal, interest and time being given

TO FIND THE RATE PER CENT.

Ex. Let $10 be the principal, 40 cents the interest and.
the time 8 months.

Analysis. $1 will draw one-tenth of the interest ; hence,,

40-^-10=4 cents; now, since $1 has drawn 4 cents in 8 mo.,

it can only draw -^ of 4 in 1 month ; thus, 4-^8=*=^ ; now,,

since J expresses what $1 has drawn in one month, it will

draw 12 times ^ in 12 months; thus, ^y(12='^^=G, the rate.

Hence we have the following

Mule. — Divide the interest Tjy the principal and the quotient
'by the time, and multiply the last quotient &y 1 2, and the pro-
duct will be the rate sought.

AND RAIL ROAD CALCULATOR. 85

Ex. Let the principal be $40, interest $1.60, time 6 mo. ;
required the rate. Ans. 8 per cent.

Operation, .|1.60-f-$40=4 cents. 4:^Q=IX12=^^=S per
cent.

Wote 1. — It will be observed that this operation proves
the example under the next preceding rule.

JSfote 2. — Most states have established a certain rate per
cent, by law; this is called legal or lawful interest.

PABTIAL PAYMENTS.

CVI. Partial pnyments are parts of a note or bond paid at
different times, and endorsed upon its back. The princi-
ples involved in computing the interest on partial payments,
make it convenient to divide the rule adopted by the Sup-
reme Court of the United States, and most of the States in-
to two parts or two rules.

WHEN THE PAYMENT OR PAYMENTS EXCEED THE INTEREST.

CVII. Rule I. — Compute the interest on tJie principal, from
the date of the note to the date of the first payment, and then
from the amount, suMract the payment, and the difference will
he the new principal; continue the operation in a similar way,
till theMme of settlement, and the last amount will he what re-
m.ains due.

WHEN THE INTEREST EXCEEDS THE PAYMENT.

CYIII. Ride. — Compute the interest as lief ore, hut pay no
attention to the pjayment, till the second payment is reached,
and then if the sum of the payments exceed the interest; from.
the amount, subtract the amount of the payment, and tlie dif-
ference wi/l constitute a neiD principal with which proceed as be-
fore, till the time of settlement he reached.

Ex. On a certain note dated January 1st, 1870, whose

86 THE MAN OF BUSINESS

face calls for $20, with interest, at 6 per cent., having 12
months to run, were endorsed the following payments:-
April 1st, 1870, $8. On August 1st, 1870, $5. On the first
of November, 1870, $4. What will remain due January 1st,
1871?

Operation, $20X1=10 cts.XB months=30+$20=$20.30,
the amount— $8=$12. 30, second principal; $12.30Xi=
.615X4 months=.246+$12. 30=112.546— $5=17.546, third
principal; $7.546X2=.3773X3 months==$113; 7.543+.113
=$7.659— $4.=$3.659, fourth principal; $3.659X'i=
. 01829 JX3 months=. 036; $3.6o9+.036=$3.695+, answer.

The following symbolic formulas will perhaps afford some
aid in understanding the above rules. Let P symbolize
the first principal ; the figured P's, the consecutive princi-
pals respectively; I, the interest, and A, B, C, D, &c., the
several payments.

FORMULAS.

CIX. I. P+I— A=2P; 2P4-J— B=3P; 3PXJ— C=
4P ; 4P-|- J==to the sum due at the time of settlement.

II. P+J— A+B=2P; 2P+J— C+D=3P; 3P;j-J=to
the sum due.

Note 1. — It will often happen in the same operation that
both parts of the rule will have to be applied.

Note2i. — The number of letters symbolizing the endorse-
ments on a note, must vary with the number of payments.

Note 3. — In order to insure accuracy in the operations, it
would be well to prove each partial operation before form-
ing a new principal.

AND RAIL ROAD CALCULATOR. S2

COMPOUND IKTEKEST.

CX, Compound interest is the interest computed on-
the amount; i. e., every successive amount becomes a new
principal, and the number of principals thus found, will.
depend on the number of intervals involved in the time
which the note or bond has been on interest.

The length of time which a note has to run before the
interest is added, and a new i)rincipal formed, will depend
on the time stipulated by the parties concerned.

When the interest is added at the end of each year, it is
said to compound annually, and when it is added at the
end of each half year, it is said to compound semi-annur
ally, etc.

TO FIND COMPOUND TNTEEEST.

CXI. Rule. — Find the interest on the principal, as in sim-
ple interest; add the interest thus found to the principal ; on
this Oj-mount proceed as l)efore ; and from the last amount sub-
tract the given principal, and the difference will do the com-
poundinterest sought.

Ex. What is the compound interest on $300 for 3
years at 6 per cent. ?

Operation, $300X6=$18.00-f |300.00=$318.00, second

principal; |318X6=S337.08, third principal ; $337.08X<3=

$20. 2248+337. 08=-$357. 3048, amount for 3 years; ^357.-

3048— $300. 00=-$57. 3048, answer.

Note 1. — When partial payments have been made on
notes at compound interest, it is customary to Jind the
amount of the giten principal, and from it to subtract the sum
of the several amounts of the endorsements.

88 THE MAN^ OF BUSINESS'

Note ^, — ^Though compound interest is nr^^t geneTaliy
favored by the law, it is not usurious. A contract or
promise to pay money with compound interest caffiSiot gen-
erally be enforced, being only valid for the principal and
legal interest. In this State, however, the money of wa^rds^
is allowed to draw compound interest.

EXAMPLES.

CXII. 1. What is the amount of $100 at 6 per cent, per
annum, compound interest, for ten years, the interest be-
ing payable semi-annually? Ans. ^112.55.

2. What is the compound interest on $G30 for four years

at 5 per cent.? Ans. $135,769.

Note. — Operations in compound interest are proved by
dividing the amount by the amount of one dollar for the
given time and rate, and, if correct, the quotient will be
the first principal.

TRUE DISCOUNT.

CXIII. Discount is an allowance made for the payment
of money before it becomes due.

There are three things involved in discount, viz : the
face of the note, the present worth, and the discount.

The face of the note is the amount specified in the note.

The present worth is what the face of the note is worth
at present in cash, and is the difference between the face
and its discount.

The discount is the difference between the face of the

note and its present worth.

Note. — The simple interest on the face of the note is not
its true discount. Simple interest expresses the fractional
part of the principal indicated by the rate per cent., the

AND KAIL EOAD CALCULATOR. 89

rate being the numerator, and 100 being the denomiTiator,
as --; but the discount expresses the fractional part of the
face of the note, as indicated by the rate per cent. ; but
the denominator of the fraction is lOO+therate thus, — .

THE FACE OP THE NOTE, IIA.TE, AND TIME GIVEN TO FIND
THE PRESENT WORTH.

CXIV, Ex. What is the present worth of $2^4, having
2 years to run, at 6 per cent. ?

Now, since the present worth expresses the present -value

of the face of the note, it follows that the face of the note

divided by $1, its interest for the given rate and time,

must give $1 of present worth for each time it is contained

in the face of the note; thus, S224^($l-f 12 cts.)=^3(0.00;

hence we have the following

Rule. — Divide the face of the note ty the amount of Si for
the given rate and time, and the quotient will he the present
worth.

Ex. What is the present worth of $327.00, having 1 year

and 8 months to run, at 6 per cent. ?

Operation, ^327.00-^1.09, (the amount on $l)=$300.00ans.

Note. — The discount is found by subtracting the present
"Vforth from the face of the note; thus, as in the example
of the above: $327.00 (face of the note,)— $300.00 (present
worth) =^27 (discount.)

EXAMPLES FOR PRACTICE.

CXV. What is the discount on $75.50 for 2 years, 6
months, at 8 per cent.? Ans. .'■fl2.58^.

What is the discount on $100.00, due 6 months hence, at 6
percent.? Ans. ^2.913.

^0 THE MAN OF BUSINESS

I bought a bill of goods on 6 months' credit, amountiiag
to $973.50; how much ought to be deducted if cash is paid
at the time of receiving the goods, interest being 6 per
cent.? Ans. $28.35.

• "What is the present worth of $940.00, having 6 monthi
to run, at 6 per cent. ?

THE PRESENT WORTH, RATE, AKD TIME GIVEN TO FIND

THE FACE.

CXVI. Rule. — Compute the interest on the present worth
at the given rate and time, add the interest to the present worth,
and the amount will te equal to the face of the note.

Ex, The present worth of a certain note of $200.00, the
time 2 years, and the rate 6 per cent. ; required, the face of
the note. Ans. $2S4.00.

Operation, $200X6=$12X3 yrs.=$24X$200=-$324.00.

Note. — This operation is the proof of the next preceding
rule.

BANK DISCOUNT.

CXVII. Bank discount differs ixoxritrue discount in this
particular: in the former, interest is computed on the face
of the note, and in the latter, on the present worth or value.

TO FIND BANK DISCOUNT.

CXVIII. Rule. — Add 3 days., called days of grace., to the
time the note has to run., then compute as in simple interest.,
and the interest thus found will he the discount sought.

Note. — The difference between the face of the note and
the discount '\% Q,QX\.Q,^i\iQ present worth ov proceeds.

Ex. Find the bank discount on $150 for six months, at

6 per cent. Ans. $4,575.

Operation, $150X^='3'5X6^ months— $4,575.

AND BAIL ROAD CALCULATOR. 91

2. If I deposit a note of $600 in bank, discounted at 6
per cent., what sum ought I to receive? Ans. $590.70.

3. Find the bank discount of $375 for 3 months and 9
days, at 7 per cent. Ans. $7,438.

4. A note for $1800, payable in 60 days, was discounted
at a bank, at 6 per cent., what was received for the note ?'
Ans. $1781.10.

5. What is the bank discount of $300, discounted at 10"
per cent. ?

TO FIND THE PACE OF A NOTE.

CXIX. Rule. — Divide the present worth or proceeds %
the present worth of one dollar for the given rate and time, and
the quotient will ie the face of the note.

Ex. I wish to borrow $590.70, discounted at 6 per cent. :
required the face of the note to be deposited. Ans, $600.

Note. — It will readily be perceived that this and the next
preceding rule mutually prove each other.

2. If I receive $550, discount being at 10 per cent.,
what is the face of the note ?

EQUATION OF PAYMENTS.

CXX. Equation of payments is a process by which we
ascertain the average time for payments of several sums,,
due at different times.

Suppose I owe $1000, of which $100 are due in two
montha, $250 in four months, $350 in 6 months, and 1300
in 9 months. If I pay the whole sum at once, how many
months' credit ought I to have?

Analysis. A credit on $100 for 2 months is the same as

92 THE MAN OF BUSINESS

a credit on $1 for 200 months ; thus, $100X3 months=200
months. A credit on $250 for 4 months is the same as a
credit on $1 for a thousand months; thus, $250X4 months
=1000 months. A credit on $350 for 6 aconths is the same
as a credit on ^1 for 2100 months; thus, $350X6 months
=2100 months. A credit on $300 for 9 months is the same
as a credit on II for 2700 months; thus, $300X9 months
=2700 months. $100+$2504-$350-f =$1000. 200 months
+1000 months+2100 months+2700 months=6000 months.
Hence I ought to have the same as a credit on $1 for &000
months; but, if I wish a credit on $1000 instead of II, it
is evidently to be for only — - of 6000 months, which is

6 months ; hence we have the following

Rule. — Multiply each payment l)y the time it has to run,
divide the tsum of the several products h/ the sum of ths 'pay-
ments, and the quotient will he the equated time.

Ex. A owes B $160; $80 have two months to run; $80

4 months ; $30, 6 months : required, the equated time.

Operation, $80 X 3 months == 160 month*.

$50 "4 " " 200

$30 " 6 '' " 180

$160 540 "

Again, 540 months+160 dollars=3| months, answer.
Proof. Compute the interest on the sum of the payments
for the equated time, and also on each payment for the time
it has to run, and, if correct the sum of the interest of the
several payments, will be equal to the interest of the sum of
the payments for the equated time, or the interest of $1 for

AND RAIL ROAD CALCULATOR. 93

the entire number of months, will equal each of the othfers ;

thus, $160 X 2- = 80 cents >< 3| months = $2.70
80 " i " 40 " " 2 '^ ^' 80
50 " i " 25 " " 4 " '' 1.00
30 " J " 15 " " 6 " " 90

$2.70
Or, $1 X ? = i cent X 540 months = $2.70

TO FIND THE TIME FOR ANY PRINCIPAL AT A GIVEN RATE, TO

DOUBLE ITSELF.

CXXL Now, since the rate percent, is equal to the num-
ber of cents which a dollar will draw in one year, it follows
that at one per cent., a dollar will draw but 1 cent in a
year, consequently it will require 100 years to draw 100
cents or to double itself.

Now, it is obvious that it will require but ,. of the time
for any principal to double itself at 5 per cent., which is
required at 1 per cent., and, since it takes 100 years at 1 per
cent, to double itself, then, if we divide 100 by 5, the quo-
tient will be the time required for any principal to double
itself at 5 per cent. ; thus, 100-1-5=20 years, the time re-
quired; hence we have ihe following

Mule. — Divide 100 hy the rate per cent.., and the quotient will
le the time required for anyprincijjal to double itself.

Ex. How long will it take a principal to double itself at

6 per cent. ? Ans. 16 1 years equal to 16 years and 8 months.

MENSURATION. — DEFINITIONS.

CXXII. 1. A ^otTiHias position only.
2. A line has length only.

M THE MAN OF BUSINESS

3. A straight line is the shortest distance between two
given points, as the line A B.

4. A curved line changes its direction continually; as, the
line C ^D.

5. An angle is the opening of two lines meeting in a point.

6. A right angle is formed by a straight line and one per-
pendicular to it, as the angle

B— c

7. An acute angle is one less than a right angle, as the

y^ B
angle E:_ c

8. An oUuse angle is one greater than a right angle ; as,

angle

Mensuration is divided into two parts, viz : mensuration
of surfaces and mensuration of solids or volumes.

MENSURATION OF SURFACES.

CXXIII. A surface has but two dimensions — length and
breadth, and is measured by means of a square as the unit
of measures.

It is applicable to the measurement of every thing in
which surface onijris concerned.

Every portion of surface may be regarded as bounded
either by right lines or by curves.

AND EAIL BOAD CALCULATOE.

LAND MEASURE.

CXXIV. The square is the simplest form
of geometrical figures ; it is bounded by four
lines of equal dimension having all its ang-
les, right angles. (See figure 1.)

TO FIND THE AREA OP A SQUARE, &C.

CXXY. The area of the square, and that of all its spe-
cies called parallelograms, is found by multiplying its two
dimensions together or base and perpendicular, and the
product will be the area or surface in the same denomina-
tion as the given dimensions. (See square measure rule 1.)

Ex. How many acres are there in a piece of ground 20
rods square? Ans. 400 rods=2 acres 2 roods.

This, and similar operations, may be proved by dividing
the area by one of the dimensions, and the quotient will be
the other.

2. In a certain piece of ground containing 5 acres, one of
its sides is 40 rods long; required the other? Ans. 20 rods.

3. A certain piece of ground is 80 cliains long and 30
wide; required the number of acres? Ans. 240 acres.

A triangle is a figure bounded by three straight lines.
(See figure 2.) Fig. 2. ^

TO FIND THE AREA OF A TRIANGLE.

CXXVI. Now, since a triangle is equal to two right ang-
les, it follows that every rectilineal figure must be equal to

i)6 THE MAN OF BUSINESS

Iwo triangles (see figure 1, diagonal D, B) ; consequently,

the area of a triangle can only be half as much as that of a.

square or parallelogram; hence, we have the following

Bule. — Multiply the altitude hy Jialf the dase, the product
will he the area sought.

Ex. The base of a triangle is 50 yards, and the perpendi-
cular 30 yards; what is the area? Ans. 750 square yards-
Operation, 25X30=750.

2. How many acres are there in a triangular piece of
ground whose base is 40 rods, and altitude 35 rods? Ans.
4 acres 1 rood 20 rods.

THE AREA AND ONE OP THE DIMENSIONS GIVEN TO FIND THE

OTHER.

CXXyil. Rule. — Beduce the area to the denomination in-
dicated hy the given dimension^ and the quotient will de the other.

Ex. In a certain triangular piece of ground containing 7

acres, whose base is 60 rods; required the altitude? Ans.

37^ rods.

Ifote. — Any one of the sides of a triangle may be assumed
as the base.

TO FIND THE AREA OF A TRIANGLE WITH THE PERIMETERS
OR THREE SIDES GIVEN.

CXXVIII. Rule. — Take half the sum of the sides, subtract
each side from it; multiply the three remainder's, and half the
sum together ; extract the square root of the product; this will he
ihe area in square units.

Ex. Sides 1 foot 10 inches; 2 feet; 3 feet 2 inches. Ans.

1 square foot, 102 square inches.

A trapezoid is a figure of 4 sides, two of Fig. 3.
which are parallel, but unequal, and are called / v

the basis. (See figure 3.) / \

AND EAIL EOAD CALCULATOR. 97

TO FIND THE AREA OF A TRAPEZOID.

CXXIX. Rule. — Take the half the sum of the basis, and'
multiply it by the nllitude after expressing them in the same de-
'>'* omination, and the product will be the area in square units of
the same kind.

Ex. What is the area of a trapezoid whose bases are 45

rods and 35, and altitude 20 rods? Ans. 5 acres.

Operation, 45+35=80-^2=40X20=800-^160=5 acres.

TO Fi:CiD THE AREA OP ANT IRREGULAR FIGURE BOUNDED BY
FOUR STRAIGHT LINES OR MORE.

CXXX. Rule. — Resolve the area of the figure into tri-
angles, ana the sum of the areas of the several triangles, will
be the area sought.

A circle is a portion of a plane bounded by a B Fig. i
curved line, every point of which is equally
distant from a point within called the cen-
tre ; the curved line A, B, C, D, is called A\
the circumference; the point C, the center;
the line A B passing through the center, the
diamater, and 0 B, the radius. See fig. 4.

THE DIAMETER OF A CIRCLE BEING GIVEN TO FIND THE CIR-
CUMFERENCE.

CXXXI. Rule I. — Multiply the diameter by ~, and the
product will be the circumference.

Ex. What is the circumference of a circle whose diameter
is 14? Ans. 44, the circumference.

THE CIRCUMFERENCE BEING GIVEN TO FIND THE DIAMETER.

Rule IL— Multiply the circumference by ~, and the product
will be the diameter.

98 THE MAN OF BUSINESS

Ex. The circumference of a certain circle is 66 feet ; re-
quired the diameter? Ans. 21, the diameter.

Note. — This rule is the converse of the former, and the
two rules mutually prove each other.

THE DIAMETER BEING GIVEN TO FIND THE AREA OP A CIRCLE.

CXXXII. Rule. — Find the circumferenae hyrule the first;
"multiply the circumference and diameter together., and divide
the product hy 4, and the quotient will he the area; or multiply
the square of the diameter l)y r^ and the product will "be the
area sought.

Ex. The diameter of a circular piece of ground is 35

rods : required, the area. Ans. 962i rods=6 acres, 2—

rods.

Note.— li the above rules are not perfectly accurate, they
approximate so near correctness that no error of any conse-
quence will result from their use ; nor am I aware that the
exact relation of the circumference to the diameter has
ever been determined; but one thing is certain, that much
labor and time will be saved by their adoption.

FLOORING, CEILING, ROOFING AND CARPETING.

CXXXin. , How many feet of plank, allowing i for

dressing, will be sufficient to floor and ceil* a room
whose dimensions are 30 ft. by 20 ? Ans. 1333 J^ feet.

Operation, 30X20=600X2=1200 feet, number of square
feet in both floors; }^—l=l- 1200 feet— 1=1333^ feet.

' 10 10 10 ' '10 •*

Hence when a deduction is to be made for waste in dress-
ing, we have the following

* Overliead ceiling is meant.

AND BAIL ROAD CALCULATOR. 99

Rule. — F'.nd the number of square feel in the floors ; suh-
iracl the fraction denoting the waste in dressing from a unity
■and divide the 7iumber of square feet iyi ike floor or floors hy
the remainder, and the quotient will he thenumber sought.

Ex. How many feet of rough plank will be sufficient to
floor a room 24X18 feet, allowing L for dressing? Ans.
480 feet.

2. How many yards of carpet, three quarters wide, will
be sufficient to carpet a floor 24 feet by 18? Ans. 64 yds.

Operation, 24X18=432 square feet ; 432-^9=48 square
jards ; 48-f-|=64 yards.

TO FIND THE NUMBER OF YARDS AT A GIVEN WIDTH TO CAR-
PET A FLOOR OP GIVEN DIMENSIONS.

CXXXIV. Rule. — Find the number of square yards con-
tained in the floor ; divide by the width of the carpet^ and the
quoti&nt will be the number of yards sought.

Ex. How many yards of carpet will it take, 5 quarters

wide, to carpet a floor 27 feet by 16? Ans. 36^ yards.

2. What must be the length of a room 18 feet wide that
64 yards of carpet, 3 quarters wide, will cover. Ans.
24 feet.

Operation, 64XI=48X9--=432-^18=24, the length of the
room.

3. How many yards of paper § wide, will paper a room
16 feet by 14, and 7 feet high?

Ans. 127 yards, 3 quarters and I'L na.

Note. — In roofing or house covering, it is customary to
make shingles 4 inches wide, and to ghow 6 inches ; and to
make rafters \ of the width of the house, and both rafters
being taken together are equal to 1 of the width of the

house.

100 THE MA]S^ OF BUSINESS

Ex. How many shingles will it require to cover a house
24 feet by 15? Ans. 2880.

Operation, 15X^=30X24=480-:- 1=2880. Hence we

have the following

Rule. — Multiply the vndih by '- and the product hy the
lengili of the roof ; divide hy 1 of a foot, and the quotient will
he the number of skijigles sought.

Ex. How many shingles will be necessary to cover 40
feet by 24? Ans. 7680.

Note. — The same result may be obtained by reducing
the number of square feet in the roof to square inches, and
dividing by the number of square inches in a shingle ; but
this would be quite a tedious process.

2. Required, the number of shingles necessary to cover
a house 28 feet by 16 ?

PLASTEBERS', PAINTERS', PAVEES' AKD CAEPENTEES' WOEK..

CXXXV. This work is computed by the square yard ;,
glaziers work by the squai-e foot or pane ; carpenters and
joiners work by the square yard — sometimes by the square,
which is 10 feet square, and contains 100 square feet.

Ex. What will it cost to roof a house at 40 cents per
square yard, 30 feet by 24? Ans. $41. 865.

2. "What will it cost to plaster the walls of a room 20
feet by 12 and 8 feet [high, at 20 cents per square yard, no
deductions being made for doors and windows? Ans.
$11. 33^

3. What will it cost to ceil a room 30 feet by 20, 8 feet
high, at $2 per square? Ans. $28.00.

4. Find the cost of paving the floor of a court-room 50'
feet by 20 feet and 6 inches, at 75 cents per square yard?: ^
Ans. $85.41i. '

AND EAIL KOAD CALCULATOR. 101

BOARD MEASURE.

CXXXYI. Board measure is applied to the measurement
of timber oi lumber sawed.

TO MEASURE IXCH BOARDS AND BOARDS LES3 THAN AN INCH

IN THICKNESS.

CXXXVII. Regardirsg inch boards as the standard or

unit of comparison, we have the following

Rule. — Multiph/ the leyi.gth and width together, and the pro-
duct 'Will he the 'tinmher of square inches or feet sought,

Ex. Required, the number of square feet in an inch

board 12 feet long and 8 inches wide? Ans. 8 feet.

Operation, 12X8=96 ; 96^12=8 feet.

Note. — Such operations may be facilitated by reducing
the inches or primes to the fraction of a foot; thus, 12X1
=8 feet.

Note 2 — In order to find the number of feet in any pile
or lot of luml)er, the most accurate method is to find the
numljer of square feet in one board ; multiply this by the
number of boards in the pile or lot.

Ex. Required, the number of square feet in a lot of

boards numbering 42, each board being 14 feet by 10

inches. Ans. 490.

Note 3. — Divide the number of square feet by one hundred,
or simply separate 2 figures on the right hand, the figures
on the left will express the number of hundreds, and those
on the right the fraction of a hundred.

Rem. It is customary, I believe, to buy and sell inch

bop.rds and those less than an inch in tliickness at the

same price.

TO MEASURE LUMBER MORE THAN AN INCH THICK.

CXXXYIII. Let it be required to find the number of

102 THE MAN OF BUSINESS

square feet in a piece of lumber measuring 12 feet by ^

inches, 2 inches thick?

Analysis. Now, it is obvious that if the board were 12

inches or one foot broad, there would be as many square

surface feet as there are linear feet ; but as the board is but

6 inches, or one-half foot wide, it will require 2 feet in

length to make one square foot ; then, if we divide the

number of feet 12X3, the quotient will be the number of

square surface feet in the board, regarding it as an inch

board ; but, the board is two inches thick, consequently it

would make 2 such boards if split or divided into two,

each one of which would contain 12 square surface feet.

Now, by multiplying the number of surface feet in the

board by 2, the product will be equal to the sum of two

such boards one inch thick ; thus, 6X2=12. Hence we

have the following

Rule II. — Find the square surface feet hy rule I; mvltipl'^
the number of feet thus found hy the thickness of the Ijoard ex-
pressed in inches^ and the product will he the number of feet
sought.

Ex. How many feet are there in 3 pieces of lumber 15
feet long 10 inches wide and 3 inches thick? Ans. 1122 ft-

Operation, lbXl='^^ feetX^ inches=37l number of feet
in one piece ; 372 X 3 pieces=112^feet.

The correctness of this rule may be tested by resolving
each piece of lumber into 3 inch boards making 9, and find-
ing the number of 9 inch boards of equal dimension, which
will equal the number of feet found in the example above ;
thus, 15X6^125X9=112^, the number of feet sought.

2. What will a lot of lumber amount to containing 25
pieces 14 feet long, 8 inches wide and 3 inches thick, at $1
jper hundred feet? Ans. $7.

AND BAIL ROAD CALCULATOR. 103

3. Required the cost of a lot of inch boards numbering

73, each measuring 12 feet by 9 inches, at 67i cents per-

hundred? Ans. $5.67,

Note 1. — If a fraction occur in the thickness of a board,,
reduce it to an improper fraction, and proceed as before ;
thus required the number of feet in a board 13 feet long 8
inches wide, and 1^ inches thick. Ans. 12 feet.

Operation, 12X^=8; 8X15=^12 feet.

Note 3. — If tlie hoard is tapering, take half the sum of the
width of its ends for its width.

Ex. What are the contents of a tapering board 20 feet
long one of whose ends is 34 inches wide, and the other 10.
inches? Ans. 20 feet.

Operation, 14+10=24-^2=12; 12 in.=l footX30=20 ft. .

Note 3. — If the plank, joist, &c., is tapering in width, ,
take half the sum of the width of the ends for the width,
and, if the tapers be both of the width and thickness, the
common rule of obtaining the contents in cubic feet is to
midtiply half tJie sum of the areas of the two ends Inj the length,
and divide the product hy 144.

Ex. How many feet in a beam 20 feet long 10 in. thick

whose width tapers from 18 to 16 inches. Ans. 283^ feet.

Operation, 18+16=34-+2=17x20=340-i-12=28iXl<)=
283i.

MENSURATION OF LOG OR ROUND TIMBER.

CXXXIX. WJien fhe log is of uniform girth.
Rule I. — Multiply the area of one end hy the length of the
log, and the product will he the numher of cuhic units

Ex. How many solid feet in a log 21 in. in diameter and

16 feet long? Ans. SSk feet.

Operation, 21 in.=^ of afootX','==5^XI='J+4=^'3^Xl6=38^,

382. (See rule IV for finding the area of the circle.)

104 THE MKN OF BUSINESS

WTien the log is not of uniform girth.

Rule 11. — Multiply the length talcen in feet hy the square.^ of
\ of the mean girth taken in inches^ and this product divided
hj 144 will give the contents in cubic feet.

Ex. If a stick of timber is 50 feet long, and its mean
girth 56 inches; what number of cubic feet does it contain?
Ans. 68/3.

Operation, 56^4=14X14=1 96> 50=9800-f-144=68,V

Note 1. — The girth of a tapering log is usually taken about
^ the distance from the larger to the smaller end.

Note 2. — The above rule is not perfectly accurate, though
it is the one generally used by business men.

3. How many cubic feet in a stick of timber which is 30
feet long, and whose mean girth is 40 in. ? Ans. 30g feet.

3. How many cubic inches in a log of wood 24 feet long,
and whose mean girth is 22 inches?

MENSURATION OF SOLIDS OR VOLUMES.

CLX. This measure is used for finding the solid contents

of bodies, and capacity of rooms, boxes, &c., and involves

three dimensions, namely : length, breath, and thickness ;

hence, to find the solid contents of bodies, we have the

following

Mule. — Multiply the three dimensions together., and the pro-
duct will de the cubic units sought., whether inches., feet., yards.,
<Sx.

Ex, How many cubic inches are there in a block of wood
6 in. long, 4 in. wide, and 3 in. thick? Ans. 72 inches.

Operation, 6X4=24X3=72.

Proof. Divide the solid contents by the product of twa
of the dimensions, and the quotient will be the other ; thus,
72-^4X3=12=6 and so on.

AND EAIL EOAD ^ALCULATOK. 105

2. What would it cost to dig a cellar 30 feet long-, 8 feet
wide, and 6 feet deep, at 2 cents per solid foot? Ans. $16.80,

3. What will a pile of wood come to, 16 feet long, 8 feet
high, and 4 feet thick, at $2 per cord? Ans. ^8.

CRIB AND BOX MEASURE.

€LXI. To find the, numler of lusJtels which a box, crib, or
tin will contain.

Bute. — Multiply the number of cubic feet by 5, and the pro-
duct will be tlie number of bushels s&ught.

Ex. How many bushels of grain can be put into a box 6
feet long, 4 feet wide, and 3 feet deep? Ans. 57 bushels,
3 pecks, 3 J- quarts.

Note. — If the corn is in the ear to find the number of
bushels in shelled corn, multiply by \ instead of \. •

Ex. How many bushels of corn will a crib hold 20 feet,
6 in. long, 4 ft. wide, and 8 feet high? Ans. 26?j bushels.

Operation, 20 feet 6 in.=20i feetX4==82X3-=656X5=
262^ bushels.

Note 2. — Though the above rule is not perfectly accurate,
yet it is sufficiently so for all practical purposes ; in order
to be perfectly accurate, the solid contents of the crib or
box to be measured, must be reduced to cubic inches, and
divided by 2150:^, the number of cubic inches in a bushel,

TO riND THE CONVEX SURFACE OF* A CONE OR PYRAMID.

CLXII. B,ul€. — Multiply the perimeter or circumference of
tlie base by half of the slant height, and to the product add the
area of the base.

Ex. What is the convex surface of a cone whose slant

height is 20 feet, and the diameter of whose base is 9 feet?

Ans. 90 feet.

106 THE MAN OF BUSINESS •

TO FIND THE VOLUME OF A CONE OR PTKAMID,

CLXIII. Bule. — Multiply the ana of the lase lyy \ of the
altitude.

Ex. What is the solidity of a cone whose slant height is
12| feet, and the diameter of whose base is 2i feet. Ans^ ,
20.45 feet +.

mason's and bricklayer' b work.

CLXIV. Mason's work is sometimes measured by the
cubic foot, and sometimes by the perch which is I62 feet
long, and Ik wide, and 1 foot deep, and contain IG^Xl^X
l=24i cubic feet.

TO FIND THE NUMBER OF PERCHES IN A PIECE OF MASONRY.

CLXV. Rule. — Find the solidity of the wall in cubic feet "by
the rules given for the mensuration of solids^ and divide ?^ 24|.,

Note. — Brick work is generally estimated by the thousand
bricks, usual size being 6 inches long, 4 inches wide and 2
or 2J thick. When bricks are laid in mortar, an allowance
of one-tenth is made for the mortar.

Ex. How many perches are there in a wall 100 feet long,

5 feet high, and 2 feet thick? Ans. 40 JJ perches.

TO FIND THB NUMBER OF BRICK NECESSARY TO MAKE ANY
PIECE OF MASONRY. J'

CLXVI. Rule. — Find the number ef solid feet hy the rule
already given, divide by the number of inches in a hrich reduced
to the fraction of a cubic foot, and the quotient will be the num-
ber of brides, but, if an allowance is to be made for mortar, mul-
tiply the number of bricTcs hy l^^, and the product will be the num-
ber required.

AND EAIL ROAD CALCULATOR. lOT

Ex. How many brick 8 in. by 4, and 2i in. thick, will be
required to build the walls of a houso 30 feet by 20, 16 feet
high, and 18 in. thick; no allowance being made for mor-:
tar. Ans. 56,000.

Note. — Add the length and iridth together, and multi])ly ty
2 ; the product will l)e the entire length of the zcall.

Operation, 100X16—1600X5=2400-^^^=56,000.

Note 2. — In the walls of a house an allowance must be
made for doors and windows, which must be determined
by the dimensions of the doors and windows given.

2. Required, the cost of a brick wall 150 feet long, 8

feet 6 inches high, 1 foot 4 inches thick, allowing A for

mortar, at $7 per thousand? Ans. ^289.17.

HEIGHTS AJSTD DEPTHS MEASURED BY THE VELOCITY OF FALL-
ING BODIES.

CXLYIL A body falling from any height towards the
earth, will fall during the first second 16 feet, and continue
to increase in velocity throughout its entire course. The
law of acceleration is expressed by the odd numbers 1, 3, 5,
7, &c.

If we take the complement* of three odd numbers, as J,
\ L, &c., the relation of the numerator to the denomina-

tor will express the comparative increase of velocity during
each consecutive second ; for instance, in each J the numer-
ator expresses the comparative distance a body will fall in the
first second, and the denominator the comparative distance
in the second second; thus, i=H; hence, if we multiply

* Tbe complement of a number is the quotient of a unit divided by that
iminber. ,

,i^''

108 THE MAN OF BUSINESS

16 by the odd numbers 1, 3, 5, 7, &c., the product will be
the distance the body will fall each successive second;
thus :

16 X 1 = 16 first second.

16 " 3 " 48 second "

16 " 5 " 80 third

16 -'7 " 112 fourth "

256
The sum of these numbers is equal to the distance (256)
which a body falls during 4 seconds of time. Now, if we
square the time 4 seconds, and multiply the square by 16,
it will be equal to the sum of the several numbers ; thus,
4X4=16X16=256, the space.

THE TIME IN SECONDS BEING GIVEN TO FIND THE SPACE.

CXLYIII. B.jj'L'E.— Square the time exj^ressedin seconds, mid-
tiply the square hj 16, and the product will l)e the space ex-
pressed in linear feet.

Ex. If we drop a heavy body into a well, and observe
the time it is falling to be 3 seconds, required the depth
of the w^ell. Ans. 144 feet.

Operation, 3X3=9X16=144.

2. If a body, dropped from the top of a mountain, occu-
pied 5 seconds in falling, required the height of the moun-
tain. Ans. 400 feet.

THE SPACE BEING GIVEN TO FIND THE TIME.

CXLIX. Rule II. — Divide the space 'by 16, and extract the
square root of the quotient^ and the root thus found will he
the time in seconds.

AND EAIL EOAD CALCCLATOrv. 109

Ex. A body has fallen through the space of 400 feet, re-
quired, the time. Ans. 5 seconds.

Operation, 400^16=25; the square root of 25 is 5, time
required.

Note. — The second rule is the converse of the first, and
the two rules mutually prove each other.

DISTANCE MEASUKED BY THE VELOCITY OF SOUND,

CI . Philosophers have, by experiments and close observa-
t'o:i, discovered that the velocity of sound through the air, at
a mean rate, is 1130 feet per second, and that this is not
affected at all by loud or low sounds, by clear or cloudy
weather, and is but sligiitly modified by favorable or ad-
verse winds. Hence we have the following

Rule. — ^lultiply 1130 feet Ijy tlie time exi^ressed in secoiicls
ichich elapse detweeii tJie Jiash of lightDing or gim'poicder and
t!ie report caused 'by the explosion, and the pjroduct Kill he the
distance in feet.

Ex. If 30 seconds elapse between the flash of lightning

and the report of the thunder, what is the distance of the

the cloud? Ans. 6'" miles.

2. If 20 seconds elapse between the flash of powder and
the report caused by the explosion of a cannon, what is
the distance of the gun?

Note. — If the above rule is not perfectly accurate, it is
quite satisfactory in the absence of a better one.

GAUGING OF CASKS.

CLI. Gauging is the process of finding the capacity of
casks or other vessels.

Casks are generally considered to be of four varieties.

110 THE MAN OF BUSINESS

First class, having the staves nearly straight.
Second, having the staves very little curved.
Third, having the staves of a medium curve.
Fourth, having the staves considerably curved.

TO FIND THE MEAN DIAMETER IN GAUGING.

CLII. The first thing to be done in gauging, is to find the
mean diameter ; this may be done by observing the follow-
ing

Rule. — First Class. — Add the 'product of the difference be-
tween the two diameters ^^ -^ or .55, to the head diameter and
the amount will he the mean diameter. Second Class. — Add
the prodzict to the difference X ^or .60. Third Class. — Add
the product of the difference x }^ or .65. Fourth Class. —
Add the product of the difference x I'o or . 70.

TO FIND THE CAPACITY OF CASKS.

CLIII. Rule. — Multiply the square of the mean diameter in
inches^ hy the length in inches, and the product multiplied Iry
.0034, will give the capacity in liquid or wine gallons.

Ex. Required the capacity in gallons of a cask of the 4th
variety whose middle diameter is 35 inches, and head dia-
meter 27 inches, and length 45 inches. Ans. 162.6 gal.

2. How many gallons will a cask of the first class contain

whose bung diameter is 30 inches, and head diameters 28

inches, length 42 inches? Ans. 120.92-|-.

Note. — If the number of cubic inches in any vessel be
found, and divided by 231, the quotient will be the number
of gallons sought in wine or liquid measure ; but, if beer
measure, divide by 282, and the quotient will be the gallons
in beer measure.

Ex. How many wine gallons will a cubic box contaiu

AND EAIL ROAD CALCULATOR. Ill

tliat is 10 feet long, 5 feet wide and 4 feet high? Ans.
1,496,^7 gallons.

2. How many gallons, beer measure, will a cylindric ves-
sel contain whose diameter is 21 inches, and 32 in. deep?
Ans. 39 gallons.

MISCELLANEOUS.

CLIV. 1. Required the number of rails 10 feet long, 8
rails to the panel to enclose a field containing 5 acres.

Operation, 5 acres x 160 rods=800 rods-^20=40 ; 40+20

=60X2=120 rods, the circumference of the field; 2 panels

lieing allowed to the rod, 120 rods X 2=240 panels, 240 X 8

=1,920 rails.

Note. — If the circumference is given, multiply the num-
ber of rods by 2, and the product will be the number of
panels, which multiplied by the number of rails assigned to
the panel, and the product will be the number required ;
but, if the contents of the field are given in acres, reduce
them to square rods, and assume any number as one line
not greater than the sum of the two dimensions, and divide
the number of square rods by the assumed line or dimen-
sion, and the quotient will be the other dimension or line,
and then proceed as before. (See the operation.)

CAUSE AND EFFECT.

CLY. A caviM is that which produces something or causes
something to be done ; as, men, horses, &c.

2. An effect is that which results from an operation of
some cause whether known or unknown.

3. Solutions by cause and effect are much to be preferred
to the method of statements in proportion.

4. Causes are either simple or compound.

112 THE MAN OF BUSINESS

5. Compoinid causes ma}^ be reduced to simple ones by
miiltiplyiug their elements together.

METHOD OF STATING BY CAUSE AND EFFECT.

CLVI. Bule. — As the first cause is to the first effect^ so is
the second cause to the second effect.

Note 1. — The first and last terras are called the extremes,
and those intermediate, the means.

Note 2. — If the unknown quantity fall in the extremeSj
the product of the extremes must be the divisor, and the
X^roduct of the means, the dividend, and mce versa.

Ex. If 4 men, in 3 days, can build i- of a wall, what part
can 6 men build in 4 days? 4 men and 3 days, the first
cause ; i the first eff'ect ; 6 men and 4 days, the second
cause; 1, the second effect, 4X3 ,' i[ '.^X^ .* ^ ^^^ statement.

Operation, 4X3=12X1=12. divisor; 6x4=24X^=6, divi-
dend; thus, 6^12=5 of the wall, the answer.

2. If 4 men, in 3 days, can build i of a wall, how many
men must be employed for 4 days to build 2? Statement,
4 men and 3 days J^ ,' ; 1 and 4 daj^sj 5. Ans. 6 men.

2. Three carpenters, A, B and C, can build a house in 31
months; A and B can build it in 4 months in what time
can C build it w^orking alone? Ans. 28 months.

Solution, 35=^; 14-2=?? what 3 did in one month; 1-^
=i what 2 did in one month; ^ — i=/g; what C did in one
month, if C did /g in one month, it will require 28 months
to complete the work.

Suggestion. This question may be proved by adding
wdiat C did to what A and B did, and the sum will be equal
to what the three did.

AND EAIL ROAD CALCULATOE. 113

3. How many acres are there in a round field 56 rods in
diameter? Ans. 15^ acres.

Solution, 56XT=l'^6X56=9856-i-4=2464-M60 rods=l52
acres.

4. If i of 6 be 3, what will k of 30 be? Ans. 7h.
Solution, 3^6=6^=1X3 third=^x20=^"=30-f4=7i.

5. A and B have the same income, A saves | of his an-
nually, but, B, by spending $200 a year more than A, at
the end 5 years, finds himself $160 in debt; what is their
income?

Solution. ^160-^5=32; 200—32=168X8=1344.

6. 2 men, A and B, on opposite sides of a plat of ground
536 yards in circumference, set out at the same time in the
same direction, to walk around it ; A walks at the rate of
11 yards in one minute, and B, at the rate of 34 yards in 3
minutes ; how many times must B walk around before he
overtakes A?

Solution. 11X3 min. =33 yards; 34—33=1 yard-^34=^
the gain on one yard ; 533-;-2=268, distance between them ;
368-f-i4=9,112-f-536=17, the answer.

7. A fox starts up 50 yards in advance of a greyhound ;
the dog bounds away in pursuit at the rate of 12 feet a leap ;
the fox scuds away at the rate of 8 feet a leap; but the fox
makes 7 leaps while the dog makes 5 ; required the distance
the dog must run before he overtakes the fox, and the num-
ber of leaps each must make. Ans. 2, 250 feet, the distance
required; 1872 dog leaps; 262^ fox leaps.

Solution, 12X5=60 ; 8X7=56; 60— 56=4-f-60=6-o=i7, the
gain on one foot ; 50X3=150 feet distance between ; 150-^1
=2250, the distance the dog runs; 2250-i-12=1875 dog

114 THE MA^ OF BUSINESS

leaps; 3250—150=2100-^-8=262^, the number of fox leaps.

8. A certain young gentleman, it is said, asked an old
gentleman for his daughter in marriage, and received the
following answer ; there are 3 gates between us and the
orchard; go into the orchard, and gather such a number of
apples as will enable you, at the first gate, to leave h and J
an apple over, at the second gate, leave h the remainder
and i an apple over, and at the third gate leave half you
have, and I- an apple over and bring me one apple ; do this
without dividing an apple and my daughter shall be yours ;
required the number.

Solution, 1-j- 5=1^X2=3, the number he had on reaching
the last gate ; d-\-i=dh'X2=7 the number brought to the
second gate; 7~\-i=7^y(2==15, the number required. R»-
verse the order of procedure, and the proof will be easy;
thus, leave 8 at the first gate, 4 at the second, 2 at the
third, and 1 is left.

9. A certain man, at his decease, bequeathed to his 3
children, 2 sons and 1 daughter, 459 acres of land to be di-
vided among them as follows: the younger son's portion
must equal j of the elder son's, and the daughter's, | ; re-
quired the share of each

Solution, 5+5+1 reduced to a common denominator =

2? li, l£=5L; since the denominators are alike they are can-
so? 20' 20 20 ' "^

celled, and, as the sum of numerators, expresses the
number of parts into which the given number is to be
divided, it may be tr^^i^sferred to the denominator; thus,
I? ^A. and l^ ; now, the numerators express the proportional
parts to be taken thus, 459+-51=9X20=180, the elder
son's share; 9X16=144, the younger son's share; 9X15==
135, the daughter's share.

AND RAIL KG AD CALCULATOR. 115

Proof, 180+144+135=459; but, according to the concli -
tion of the question, the younger son's share must be I of
the elder son's; the daughter's, 2, thus li^==i; H5=l

10. A certain man, looking on his watch, was asked the
time of day; he replied the time past noon is equal to I of
the time pa^st midnight ; w^hat was the time? Ans. 3 o'clock.
Solution. I — 1=1- 12+^=15 hours— 12=3, the time sought.

11. A man dying, worth $5,450, left a wife and two
children, a son and daughter, absent in a foreign country ;
he directed if his son returned, the mother should have ^
of the estate, and the son the remainder ; but, if the daugh-
ter returned, she was to have i, and the mother the remain-
der ; now, it so happened that they both returned ; how
must the estate be divided to fulfill the father's intentions?

Solution, 1+3+4=7; !^5,460+7=$780, daughter's share ;
$780X2=1,560, wife's share; $780X^=3,120, son's share.

12. A traveler found a purse of money; h of its contents
was silver, I gold and $20 in greenbacks ; how many dollars
did the purse contain i?

Solution, ^+H'o; K— 'o=iO=^^20; 20X10=200, number
of dollars.

Proof, k of 200 = 100, silver;

I of 200 == 80, gold ;

Greenbacks, = 20

The sum,

RULE FOR EXTRACTING THE SQUARE ROOT.

CLYII. I. Separate the given number into periods of twa
figures^ commencing at units; the left hand period may con fairs,
hut one figure.

116 THE MAN OF BUSINESS

n. Take the square root of the left hand period for the first
figure in the root.

III. Subtract the square of this from the left hand period,
Irring down the next period ; divide the result, exclusive of the
right hand figure, ly twice the part of the root already found ;
the quotient will de the second figure of the root.

IV. Set this figure of the root on the right of the divisor;
multiply the divisor thus completed h/ the second figure of the
root ; subtract the product from the last dividend, and bring
down another period.

V. Double the root already found for a trial divisor, find
another figure of the root, and proceed as before, till all the pe-
riods have been brought down.

Ex. Required, the square root of 2809.

Op eration, 2809 (53 square root.
25

103)309
309

000
Proof. Raise the root to the second power, and the re_
suit will be equal to the given number ; thus 53X53=2809.

Note 1. — Annex periods of naughts to obtain decimals.

Note 2. — The square root of a common fraction, is the
equal root of the numerator divided by the square root of
the denominator ; but, if the denominator is not a square,
.make it so by multiplying both terms, of the faction by the
denominator ; or the root may be obtained by reducing the
common fraction to a decimal, and extracting the the root
as integral numbers.

Two brothers bought a tract of land containing 200

acres, for which they were to pay |'8O0, each paying an equal

AND RAIL ROAD CALCULATOR.

117

sum; but one end of the land being richer than the other,

the elder brother proposed to the younger that he would

pay 50 cents more per acre if he would let him have the

better portion ; this being agreed to, required the number

of acres each should receive, and the price per acre.

C Elder brother's, 93i-j-9'Cres.
. J Younger brother's, 106^ acres, nearly.

^^- ] Price of elder brother's, $4,265+.

[Price of younger brother's, $3.765-|-.

RULE FOR SOLUTION.

CLVIIl. Divide half the whole cost by the whole number of
acres, and to the square of the quotient add the square of half
ihe difference of the price per acre; then extract the square root
of the sum, and to this root add ihe quotient of half ihe whole
cost, divided by the whole number of acres. This last sum in-
creased by haf the difference of ihe price per acre, will give
ihe price per acre of the best land, and diminished b y the same,
will give the price per acre of the poorest land.

LEaA-L FORMS

NECESSAKY IN ORDINARY BUSINESS,
PKEPAEED BY

RICHARD WATT YORK, A. M.

Attorney and Counsellor at Law.

u s

affidavit.

North Carolina,

Chatham County y

Personally appeared before me, John Doe, a Justice of the'
Peace in and for the County and State aforesaid, Eichard
Boe^ who being duly sworn doth depose and say that {in-
sert here the facts as they exist.']

John Doe, J. P.

AGREEMENT.

Articles of agreement made, entered into, and concluded

upon this the — day of , 187 — , between John^Doe, of

the first part, and Richard Boe, of the second part :

First, for and in consideration of \here insert the consid-
eration as it exists whether money, property^ worh^ cfcc.,] to said"
John Doe, paid by Richard Roe, the said John Doe covenants, ,
promises and agrees to [here insert the agreement on the part'
of the first pzrty.']

Second, for and in consideration of \Jiere insert the consid-
eration as it exists whether money, property, worlc, (&g.,] to
Richard Roe paid by JaJm Doe, the said Richard Roe cove-
nants, promises and agrees to [here insert the terms of the agree •*
ment.'\

120 THE MAN OF BUSINESS

And the said Jolm Doe and Richard Roe, for themselves,
their heirs, executors and assigns, mutually covenant, pro-
mise and agree the one with the other, that they will sev-
•erally perform the stipulations as above mentioned by them
jespectively assumed.

In witness whereof, the said JoTin Doe and Richard Roe

have hereunto set their hands and seals, the day and date

above written.

Sealed and delivered in ) John Doe, {Seal.']

the preience of . \ Richard Roe, {Seal.]

AGREEMENT FOR THE SALE OF AN ESTATE IN LAND.

Articles of agreement entered into, made and concluded,
this the — day of , 187 — , between A. B. and C. D.

The said A. B. agrees to sell to the said C. D. all that
tract or parcel of land, with the appurtenances thereunto
belonging, known as the place, bounded as follows, be-
ginning at [here insert the boundaries., ] containing acres,

more or less, for the sum of dollars ; and, on receipt

of said sum of money on or before the — day of , 187 — ,

the said A. B. will execute a good and sufficient title at
law and in equity in fee simple to the said C. D. with a
covenant of general warranty as to title and against en-
cumbrances, to the said C. D., his heirs and assigns.

And the said C. D. agrees that, upon the due and proper
execution of a good and sufficient conveyance in fee simple,

he will pay the said the sum of dollars to the said

A. B. or his assigns.

In testimony of all which things the said A. B. and C. D.

AND EAIL HOAD OALOULATOK. 121

have signed their names, and affixed their seals, the day and

date above specified.

In the presence of ) A. B., fSeal.]

E. F., V C. D., [Seal]

G. H.

ARTICLES OP AGREEMENT TO FORM A COPARTNERSHIP.

Articles of agreement made and concluded on this the —
day of , 187 — , between John Den and Richard Fen.

First, the said John Den and Richard Fen have agreed
and, by these presents do hereby agree, to form a partner-
ship under the name and style of Den and Fen for the pur-
pose of carrying on the business of at .

Second, the capital stock shall consist of dollars, of

which amount John Den is to advance dollars, and

Richard Fen is to advance, [any other agreements mayl)e in-
serted as the fa£.ts in the case may justify.']

The said partnership shall continue from the — day of
. , 187—, until the — day of , 187—.

In testimony whereof, &c.

ASSIGNMENTS.

A general form of assignments by indorsement on the
back of any instrument, whether. Agreement, Mortgage,
Bond, &c., conveying personal property.

Know all men by these presents, that, I, the within nam-
ed John Doe^ for and in consideration of the sum of one dol-
lar to me paid by Richard Roe., have assigned to the said

122 THE MAN OF BUSINESS

MicJiard Roe all my interest in the within written instru-
ment, and every clause, article, or thing therein contained.
\where necessary tlie following short form of power of attorney^
Tnay de added, ] and I constitute the said Ricliard Roe, my
attorney, in my name and to his own use, to take all neces-
sary legal proceedings for the complete recovery and enjoy-
ment of the premises hereinbefore assigned, with power of
substitution.

Witness my hand and seal, the — day of , 187 — .

John Doe, {Seal.']

ASSIGNMENT, BY INDORSEMENT, OP A MOKTGAGE IN FEE.

Know all men by these presents, that I, the within nam-
ed John Den, in consideration of the sum of dollars to

me paid by Richard Fen, receipt of which is hereby acknow-
ledged, &c., have granted, assigned, released, and convey-
ed, and by these presents do hereby grant, assign, release
and convey unto the said Richard Fen the premises and
lands within conveyed to me in mortgage, and all my right,
title, interest, and estate in and unto the same. To have
and to hold to the said Richard Fen, his heirs and assigns
forever.

{Clauses of warranty, against encumbrances, for further as-
surance of title, &c. , may be added as in a common deed, if
necessary.]

Witness my hand and seal, the — day of , 187 — .

In the presence of

John Den, [8eal.\

AND RAIL ROAD CALCULATOR. 123

ABSOLUTE ASSIGNMENT OF AN ORDER BY INDORSEMENT.

I, the within named John Doe, do hereby assign end trans-
fer all my right, title and interest in and to the within writ-
ten order, and the moneys secured thereby unto Richard
Roe and his assigns. This the — day of , 187 — .

In the presence of )

. \ John Doe.

AWARD OF ARBITRATORS.

To all to whom these presents shall come : — greeting.

Know ye, that whereas, John Den^ of the County of Chat-
ham, and RieJtard Fen, of the County of Wake, did, on the-

- - day of , 187 — , enter into a bond in the sum of

dollars, conditioned to stand to and abide by the award
and decisions of the arbitrators in a certain controversy be-
tween them, [or did muiunlly agree to stand io and abide hy^,
when no bond has been entered into. ]

Now, therefore, be it remembered, that on the — day of
, 187 — , the undersigned arbitrators did hear and ex-
amine the said parties, and. having maturely and impartial-
ly considered all the matters involved therein, do make
.this our award and decision, to-wit:

1st. We do award that John Den [state the award in
jjlain languages.^

2d, We do further award that Richard Fen [here state,
again the award in plain language, and, in separate numbered
items state all the various awards ]

Given under hand and seal, the — day of , 187 — .

tS^s.^Shott, [^''^^'^^«^^^^

124 THE MAX OF BUSINEkSS

Bill op sale, with clause of warranty.

North Carolina,

Chatliain County.

Know all men by these presents, that I, Kichard Roe,

for and in consideration of the sum of dollars,

to me paid by Jno. Doe, do hereby grant, assign, convey
and transfer unto the said Jno. Doe {here mention the pro-
•perty conveyed.,') to have and to hold to the said Jno. Doe,
his executors, administrators, and assigns forever. And I
do covenant for myself, my executors, adminstrators and
assigns, to and with the said Jno. Doe, his executors, ad-
ministrators and assigns, to warrant and defend the title
hereby conveyed from the lawful claim of any and all per-
sons whatsoever. (If this Bill of Sale is given by a sheriff
or constable, he should recite in the first part the fact of
the sale under execution, and after the word ^'■iiyJiatsoever,'*
add the words, " .so far as my o-ffice and duty as (sheriff or
constable) requires, and no further.)

Witness my hand and seal the — day of — ,187 .

Richard Roe, [L. S.]

Signed, sealed and delivered in \
the presence of . S

BOND — simple.

$100.00. after date, I promise to Jno. Jones

one hundred dollars for value received. Witness my hand
and seal the — day of — , 187 .

Joseph Stark, [L. S.j
In the presence of .

AND RAIL ROAD CALCULATOR. 125

SIMPLE BOND WITH PBINCIPAL AND SURETY.

Twelve months after date, with interest from date, we,
Jno. Den as principal and Richard Roe and Richard Fen
as sureties, promise to pay Jno. Doe one thousand dollars
for value received. "Witness our hands and seals, the —
day of — 187 .

Jno. Den, [L. S.]
Richard Roe, [L. S.]
Richard Fen, [L. S.]
In the presence of .

BOND with condition.

Know all men by these presents, that I, John Den, am
held and firmly bounden unto Richard Fen in the sum of
one thousand dollars, to the which payment, to be well and
truly made, I bind myself, my heirs, executors and admin-
istrators.

Sealed with my seal the — day of — , 187 .

The condition of the above obligation is such, that
whereas, John Den hath agreed [to deliver unto Richard Fen
100 bales of cotton, weighing not less than 400 Ihs. each, on or
be/ore the first day of December, 187 .] Now if the said Jno.
Den shall well and truly {deliver the cotton as hereinbefore
recited.^ then this obligation to be null, void, and of na
efi'ect, otherwise of full force and effect.

Witness my hand and seal the — day of — , 187 .

Jno. Den, [L. S.]

In the presence of .

126 THE MAX OF BUSINESS

lien bond under act of march ist, 1867.

North Carolina, )
Chatham County. \

Whereas, A. B., of the county of , N. C, has agreed

to make advances of supplies to C. D. for the purpose of
agriculture during the year 187 , to the value and amount

of dollars ; and whereas, as the said C. D. desires to

secure to the said A. B. the said sum in accordance with the
terms of the Act of the General Assembly of North Caro-
lina, entitled " An Act to secure advances for agricultural
purposes,'' ratified the 1st day of March, 1867; therefore,
in consideration thereof, C. D. as principal, and E. F.
and G. H. as sureties, do hereby agree with the said A. B.
that he shall have an interest in and lein upon the crops of

and other products to be raised during the year

187 , upon the lands of in the county of , occu-
pied and to be cultivated by C. D. during the said year
187 to the full value of the advances to be made as afore-
said. And for further security, the said C, D. hereby bar-
gains and sells to the said A. B. the following articles of
personal property now in the possession of the said C. D.,

with the understanding that if the said C. D. shall well
and truly pay to the said A. B. the sum advanced on or
before the — day of — 187 , then the said lien shall be
discharged, and the said property revert in C. D. : other-
wise the said A. B. shall have power to take into his pos-
session said crop and other property, and sell the same for
cash after ten days notice.

In testimony of all which things the said parties have

hereunto set their hands the — day of , 187 .

A. B.

C. D.

E. F.

In the presence of . G. H.

AND EAIL EOAD CALCULATOR- 127

FORTHCOMING BOND.
IfOKTH CaEOLINA, )

'^ County. \

Know all men by these presents, that we and

are held and firmly bounden unto , sheriff

{or constable) of county, in the sum of dollars,

to which payment well and truly to be made, we bind our-
selves, our heirs, executors and administrators, jointly and

severally. Sealed with our seals the — day of , 187 .

The condition of the above obligation is, that whereas

the said , sheriff [or constable) as aforesaid, hath this

day levied an execution in favor of against the above

bounden upon the following personal property of

the said , to-wit: (here set out the various articles of

property^) and hath permitted said property to remain in

the possession of the said ; now, therefore, if the

said , on the — day of — , 187 , the day of sale ap-
pointed for the same, or upon any other day to be hereafter

named by the said , sheriff {or constable) as aforesaid,

shall well and truly deliver to said , sheriff {or con.

stable) as aforesaid, all the said personal property to answer
said execution ; then the above obligation to be null and
void : otherwise to remain in full force and virtue.

, [L. S.]

, [L. S.l

In the presence of .

128 THE MAI^ OF BUSINESS

COVENANTS

The loll owing forms may be inserted in Deeds as the
various cases may require :

Of one Person wiih one Person.

And the said Jno. Den, for himself, his heirs, executors
and administrators, and for each and every of them, doth
covenant with the said Richard Fen, his heirs, executors
and administrators, that [here insert the covenant in plain
language. ]

N. B. Sometimes the word ''assigns'' should be added
after the name of the covenantee. In covenants respecting
personal property the word ''heirs'^ should be omitted. Its
insertion, however, can do no harm, and it is bettter that
unprofessional persons should always insert it. Such per-
sons also, out of abundance of caution, might use the word
''assigns'' after the covenantee, thus: "with the said Richard
Fen, his heirs, executors, administrators and assigns.''''

A Joint Covenant with one Person.

And the aforesaid Jno. Doe, Richard Roe and Jno. Den
for themselves, their heirs, executors and administrators,
and for each and every of them, do covenant with the
aforesaid Richard Fen, his heirs, executors, administrators,
(and assigns,) that, &c.

A Joint and Several Covenant.

Same as above, except as follows: "do jointly and sev-
erally covenant," &c.

Note. — All the usual covenants in a deed will be found
under ^' Deeds."

AND EAIL ROAD CALCULATOR. 129

DEEDS.

Beed Poll, with Covenants of THte, Warranty, &c,

!NoRTH Carolina, )
Chatham County. )

Know all men by these presents, that I, Jno. Doe, of the
county and State aforesaid, in consideration of dol-
lars to me paid by Richard Roe, the receipt of which is
hereby acknowledged, have bargained and sold, granted
and conveyed, and, by these presents, do give, grant, con-
Tey, bargain and sell unto Richard Roe, his heirs and as-
signs, all that tract or parcel of land situated in

oounty and State of , lying upon the waters of ,

and bounded as follows, to-wit: beginning at [here set oui

ike boundaries and^ description of the land,] containing

acres, more or less; together with all the rights, ways,
privileges and appurtenances in anywise to said land apper-
taining and belonging. To have and to hold the above-
mentioned lands and premises to the said Richard Roe, his
heirs and assigns, to his and their use and behoof forever.

And I, the said Jno. Doe, for myself, my heirs, execu-
tors and administrators, do covenant with the said Richard
Roe, his heirs and assigns, that I am lawfully seized in fee
simple of the af oregranted lands and premises : that they
are free from all encumbrances of any and every kind what-
soever: that I have a good right to sell and convey the
same to the said Roe as aforesaid ; and that I will, and my
heirs, executors and administrators shall, warrant and de~
fend the same to the said Richard Roe, his heirs and assigns
forever, against the lawful demands of all persons what-
fioever.

130 THE MAN OF BUSINESS

In testimony of all which things I have hereunto set my

hand and seal the — day of , 187 .

Jko. Doe, [L. S.]

Signed, sealed and delivered ^

in the presence of !

Jno. Den, |

Richard Fen. J

DEED INDENTED OB INDENTURE IN FULL WITH ALL THE
USUAL COVENANTS.

This indenture made the — day of , 187 — , between

John Doe, of party of the first part, and Richard Roe,

of party of the second part :

Witnesseth, that the said party of the first part, for and

in consideration of the sum of dollars, lawful money of

the United States, to him paid by the said party of the sec-
ond part, at or before the ensealing and delivery of these
presents, the receipt of which is hereby acknowledged, and
the said party of the second part, his heirs, executors, and
administrators forever released and discharged from the
payment of the same, by these presents hath given, granted,
bargained, sold, aliened, remised, released, confirmed, and
conveyed, and by these presents, doth give, grant, bargain,
sell, alien, remise, release, and convey to the said party of
the second part, his heirs and assigns, all that tract or par-
cel of land, situate in the County of and State of ,

lying upon the waters of and bounded as follows, to

wit : beginning at [here set out the boundaries and descrip-
tions of the land,] together with all and singular the tene-

AND RAIL ROAD CALCULATOR. 131

ments, hereditaments, and appurtenances thereunto belong-
ing, or in anywise whatsoever appertaining ; and the rever-
sion and reversions ; remainder and remainders ; rents ; is-
sues ; and profits thereof ; and, also all the estate, right,
title, interest, property, possession, claim, and demand
whatsoever, as well at law as in equity, of the said party of
the first part, of, in, and to the aforegranted lands and pre-
mises with the appurtenances thereunto belonging.

To have and to hold the aforementioned lands and pre-
mises to the aforesaid party of the second part, h.l,§ heirs and
assigns, to his and their own proper use and behoof forever.

And the said John Doe, party of the first part as afore-
said, for himself, his heirs, executors, and administrators,
doth covenant with the said Richard Roe, party of the sec-
ond part as aforesaid, his heirs, and assigns, that the afore-
said John Doe at the time of the ensealing and delivery of
this indenture, was lawfully seized in his own right of a
good, absolute, and indefeasible estate of inheritance, la
fee simple, of, in, and to, all and singular the lands and ap-
purtenances hereinbefore conveyed; and has good right,
full power, and lawful authority to bargain, sell and convey
the same in manner and form as aforesaid ; and, that the
said party of the second part his heirs and assigns shall
and may, at all times hereafter peaceably and quietly have,
hold, use, possess, occupy, and enjoy the above conveyed
lands and premises with the appurtenances thereunto be-
longing, without any let, suit, trouble, molestation, evic-
tion, or disturbance, of the said party of the first part, his
heirs and assigns, or of any other person or persons lawful-
ly claiming the same ; and, that the aforesaid lands and

132 THE MAN OF BUSINESS

tenements now are free, clear, and discharged, and unen-
cumbered of and from all former grants, titles, charges, es-
tates, judgments, taxes, assessments and encumbrances of
whatsoever kind or nature ; and, that the said party of the
first part and his heirs, and all and every person or persons
whosoever lawfully or equitably deriving any estate, right,
title or interest of, in, or to, the hereinbefore-granted lands
and premises, by, from, or under, or in trust for them or
either of them, shall and will, at any time or times hereaf-
ter, upon tft« reasonable request of the aforesaid party of
the second part, his heirs and assigns, and at the proper
costs and charges of the said party of the second part, his
heirs and assigns, make, do, and execute, or cause to be
made, done, and executed, all and any such further and
other lawful and reasonable acts, conveyances, and assur-
ances in the law, for the better and more effectually vesting
and confirming the lands and premises hereinbefore con-
veyed, and so intended to be in, and conveyed to, the said
party of the second part, his heirs and assigns forever, as by
the said party of the second part, his heirs and assigns, his
or their counsel learned in the law, shall be reasonably ad-
vised and required.

And the said John Doe^ his heirs, executors and adminis-
trators, the above-described lands and premises hereinbe-
fore conveyed, with the appurtenances thereunto belong-
ing, to the said party of the second part, his heirs and as-
signs, against the said party of the first part, his heirs and
assigns, and against all and every and person or persons
whomsoever lawfully claiming or to claim the aforesaid
lands and premises, shall and will warrant and by this in-
denture forever defend.

AND EAIL ROAD CALCULATOR. 133

In testimony of all which things the said party of the first
part both hereunto set his hand and afiixed his seal, this

the — day of , A. D., 187—.

Signed, sealed and delivered ) John Doe, [Seal.]

in the presence of >

John Den, )

Richard Fen.

DEED OF QUIT-CLAIM.

This Indenture made the — day of , A. D., 187 — ,

between John Boe, of , and Bichard Boe, of .

Witnesseth, that the said John Doe^ for and in considera-
tion of the sum of dollars, to him paid by the said

Bichard Boe^ receipt of which is hereby acknowledged, hath
released, remised, and quit -claimed, and, by these presents,
doth hereby remise, release, and quit-claim unto Bichard
Boe^ his heirs and assigns forever, all that tract or parcel of

land situated in the County of and State of ,

lying upon the waters of and bounded as follows, to

wit : beginning at [here insert the description and boundaries, ]

containing acres, more or less ; together with all and

singular the tenements, hereditaments, and appurtenances
thereunto belonging ; and all right, title, or estate, claim
and demand whatsoever, as well at law as in equity, of the
said John Doe of, in, and to, the above-described premises.

To have and to hold all and singular the above-mention-

134 THE MAN OP BUSINESS

ed lands and premises unto the said Richard Boe^ his heirs

and assigns forever.

In witness whereof, &c.
Signed, sealed and delivered ) John Doe, \^Seal.'\

in the presence of >

John Den, )

KicHABD Fen.

Note. — ^Whenever interlineations^ additions or erasures are
made in drafting a deed, the fact should be noticed at the
foot of the deed thus '•'' all interlineations^ erasures and addi-
tions made he/ore signing and sealing. ^^

Note. — ^No forms are inserted for deeds of married wo-
men, sheriff's, clerk's, administrators and other officers of
the law. They always depend on circumstances for their
form. In all such cases, counsel learned in the law should
be consulted, and the deed drafted by them.

DEED IN TRUST.

This Indenture, in three parts, made the — day of ,

A. D., 187 — , between John Doe^ of the first part, Richard
Roe., of the second part, and [here should he inserted the
names of the party or parties for whom the trust is created^ in
ease of creditors it will le sufficient to say '' creditors of the said
John Doe,"] of the third part.

Witnesseth, that the said John Doe^ party of the first part,

for and in consideration of the sum of dollars, {jgen-

erally a nominal sum of "owe," *'j^ve" or "^^ti" dollars,'] to
him paid by Richard Roe, party of the second part, receipt
of which is hereby acknowledged, hath bargained and sold,

AND EAIL KOAD CALCULATOR. 135

and, by these presents, doth bargain and sell unto the said
Richard Roe^ of the second part, his heirs and assigns, all

that tract or parcel of land, situate in the County of

and State of , lying upon the waters of , and

bounded as follows: beginning at [here insert boundaries and

descriptionSy'] containing acres, more or less, \if per-^

sonal property J also is conveyed^ insert as follows '"'■ and the Jol-
lowing personal property^ to-wit :''' setting it forth explicitly .~\

To have and to hold to the said Richard Roe, of the sec-
ond part, his heirs and assigns forever.

Li trust, nevertheless, that [here insert the trusts in plain
language. If, for creditors, state all the duties which the trus-
tee is to perform, such as time, place, manner of sale, &c. ]

And the said John Doe, of the first part, for himself, his
heirs, executors and administrators, covenants with the said
Richard Roe, of the second part, his heirs and assigns, that
he is lawfully seized in fee of the abo^e described property
and premises ; that they are free from encumbrances ; that
he has good right and title to sell and convey the same ; and
that he will, and his heirs, executors and administrators,
shall warrant and defend the title to the same to the said
Richard Roe, of the second part, his heirs and assigns for*-
ever against the lawful demands of all persons.

And the said Richard Roe, of the second part, for himself,
his heirs, executors and administrators, covenants with the
said John Doe, of the first part, his heirs and assigns, that
he will well, truly and faithfully perform the duties and
trusts emunerated and specified in this deed.

In testimony of all which things the said John Doe and

136 THE MAN OF BUSINESS

the said Bicliard Boe have hereunto set their hands and

seals, the — day of , A. D., 187 — .

Signed, sealed and delivered ) John Doe, \^8eal.\
in the presence of >• Richard Roe, \8eal,\

JoBTN Den, )

Richard Fen.

DEED IN mortgage.

This Indenture made this the — day of , A. D.,

187 — , between JolmDen^ of the first part, and Richard Fen,
of the second part.

Witnesseth, that the said John Den^ for and in considera-
tion of the sum of one dollar to him paid by Micha/rd Fen^
of the second part, receipt of which is hereby acknowledg-
ed, and the further considerations which, in this deed,
hereinafter appear, hath bargained and sold, and, by these
presents, doth bargain and sell unto the said Richa/rd Fen,
his heirs and assigns all that tract or parcel of land situate

in the County of and State of , lying upon the

waters of and bounded as follows, to-wit : beginning

\here insert the descriptions and boundaries,] containing

acres, more or less. [If personal property also is conveyed,
then add here '•^and the following personal property, to-wit,'*'*
netting it forth eo'plicitly. ]

To have and to hold to the aforesaid Richard Fen, his
heirs and sssigns forever.

And the said John Den, for himself, his heirs, executors
and administrators doth covenant with the said Richard
Fen, his heirs and assigns, that he, the said John Ben, is
lawfully seized in fee simple of the above described pr^p-

AND BAIL EOAD CALCULATOR. 137

€rty and premises ; that the same is free from all encum-
brances; that he has good right to sell and convey the
N same ; that he will, and his heirs, executors, and adminis-
trators, shall, warrant and defend the same to the said
Richard Boe^ his heirs and assigns forever against the law-
ful demands of all persons whomsoever.

On condition, nevertheless, [that if the said Jno. Beriy
his heirs, executors and administrators shall well and truly pa/ij
to the said Richard Fen^ his executoi's^ administrators and as-

signSf the sumo/ dollars on or before the — day of ,

187 , with the interest, costs and chm'ges thereon accru^d^l
then this deed and conveyance to be null, void, and of no
effect; otherwise to remain in full force and effect. \_Tf a
power of sale is conferred, then add here as follows : ^'' and if
the said sum of money, or any portion thereof, hereinbefore reci-
ted^ shall de and remain unpaid at the date aforesaid, then the
said Richard Fen and his assigns shall have power to sell the
same in manner and form as follows,'''' stating the terms, time,
manner, &c., of the sale.]

And the said Richard Fen of the first part, for himself,
his heirs, executors, administrators and assigns, covenants
with the said Jno. Den of the second part, his heirs, execu-
tors, administrators and assigns, that he will well and truly
perform all stipulations contained in this deed and im-
posed upon him by the same.

In witness whereof, the said Jno. Den of the first part,

and the said Richard Fen of the secornd part, have hereunto

set their hands and seals the — day of — — , A. D., 187 .

Signed, sealed and delivered ^

in the presence of / Jno. Fen, [L. S.]

Jno. Doe, f Richakd Fen, [L. S.]

Richard Roe. ^

138 THE MAN OF BUSINESS

Note. — After the words ''on condition, nevertheless, thai,^*
in the above deed, the conditions should be set out in plain
and explicit language in that portion included between [ ]
according to the circumstances which give rise to the
mortgage.

CHATTEL MORTGAGE.

I, Jno. Doe, of the county of , and State of

am indebted to Richard Roe, of the county of , and

State of , in the sum of dollars due by [here

state whether h^ open account, note, <&c.,] which will be due on

the — day of , 187 , and to secure the due payment

of the same, I hereby convey to him the following articles
of personal property, to-wit : [here set out the articles ex-
pliciUi/.]

On condition, neverthelels, that if I fail to pay said

debt and interest on or before the — day of , A. D.,

187 , then he may sell said property, or so much thereof
as may be necessary to satisfy said debt, by public auction
for cash, after having first given twenty days' notice at
three public places, and apply the proceeds of said sale ta
the discharge of said debt, and pay the surplus, if any, to
me.

Witness my hand and seal this the — day of , A»

D., 187 .

Jno. Doe, [L. S.]
In the presence of

Jno. Den

RiCHARB

. I

Fen. >

A^D KAIL EOAD CALCULATOR. 139*

LEASE.

This Indenture made, this the — day of , A. D. 187 — ,

between John Doe, of , and Richard Roe^ of ,

witnesseth that the said John Doe doth hereby demise, lease,
and to farm let, unto Richard Roe^ that piece or parcel of
land known as [here describe the premises which are the subject

of the lease,] to hold for the term of years from the

— day of , A. D., 187 — , during the said term unto the

said Richard Roe ; yielding and paying, unto the said John
Roe or his assigns as rent and render therefor \here insert
what the lease is to pay for the use of the premises, whether a
pa/rt of the crop, Tnoney, &c., and when to he paid, whether
yemly^ half-yearly, quarterly, monthly, &c. State all these
plainly and fully.]

I. And the said Richard Roe covenants and agrees to pay
the rent as aforesaid in manner as aforesaid, to the said
John Doe or his assigns ; and to deliver up the premises to^
the said John Doe or his attorney, at the end of the term, in
as good condition as when received, reasonable wear and
tear from the use thereof, and casualty from fire, tempest
and other unavoidable cause, being excepted : that the said
John Doe, his attorney, or assigns may, at all times, enter
the premises to view the same and make improvements
thereon at reasonable times.

n. The said John Doe covenants that the said Richard Roe
shall have quiet and peaceable possession during the said
term, and that he will warrant and defend the title against
the claims of all persons as to the possession of the said pre-
mises during the said term.

In witness of all which things the said John Doe and

140 THE MAN OF BUSINESS

Hichard Boe have hereunto signed their names and aflSxed

their seals, the — day of , 187 — .

In the presence of )
John Den, > John Doe, \^8e'd.'\

RicHAKD Fen. ) Richard Roe, [/SeaZ.]

Note. — Other covenants may be inserted as may be agreed
on by the parties, the forms of which will be found below.
The covenant of the lessor for quiet enjoyment and defense
of title, as a matter of form only^ should come last in the
deed.

Covenant to pay taxes.

And the said Itichard Boe covenants and agrees to pay all
taxes and duties lawfully imposed and levied on the pre-
mises demised and let unto him during his said term.

, Covenant not to commit waste.

And the said Bichard Boe covenants that he will not com-
mit waste on the demised premises.

Covenant not to underlet.

And the said BicJiard Boe covenants and agrees that he
will not underlet the said demised premises, or any part
thereof, nor permit any other person or persons to occupy
the same or any part or portion thereof without the consent
.{"m writing,''^ if the parties so agree,] of the said John Boe
or his assigns.

Covenant under the '"''Act ^j/" 1868- 9, Sees. Id and 14, Laws of
Worth Ca/rolina, giving the Lessor a Lien on the Crop as Or
security for the rent.

And the said Bicliard Boe, for himself, his executors and
administrators, covenants and agrees with the said John Boe

AND RAIL ROAD CALCULATOR. 141

and his assigns, that the said John Boe shall have a lien up-
on the crops to be grown upon the aforesaid demised pre-
mises, and the said Roe as aforesaid hereby transfers, and
assigns to the said John Doe^ all his right, title, and inter-
est in the crops to be grown on the premises as aforesaid
for the sole purpose of constituting a lien and security on
said crop for the rents which may be now due, or may here-
after become due during the said term, as well as, and also
for the due and faithful performance of each, every, and all
stipulations contained in the said dead of demise and lease»

lien law — act op 186 9-' 70 — form op notice under
section 3. — ^notice op sale to satisfy a lien.

North Carolina, )
Chatham County, f

Whereas, the undersigned as a mechanic and artizan has
["wflwZd, altered^ or repaired ^^] the following personal prop-
erty, to- wit: [here enumerate the property,^ at the request of
John Den^ the legal owner or possessor of the same ; and, as
the costs and charges therefor have remained unpaid for the

space of days ; the undersigned will sell the same on

the — day of , 187 — , at — o'clock, at , to the

highest bidder for cash, to discharge said debt and lien,
due and owing as aforesaid.

Richard Fen*

142 THE MAN OF BUSINESS

FORMS UNDER SECTIONS 4 AND 5. — ENTRY TO BE MADE BY
MAGISTRATE OP FILING THE CLAIM.

^^r,^ <^T''"',^ I In a Jmtioe's Court.
Chatham County. )

Be it remembered that on the — day of , 187—,

personally appeared before me, John Doe, a Justice of the
Peace in and for said County, John Ben, who filed before
me the account and claim hereunto annexed, for the sum

of dollars, as a lien upon the property of Bicha/rd Fen^

under the Act of 1869-'70.

This the — day of , 187—. John Doe, J. P.

Note 1st. — Under Sec. 4, if the debt for work and labor
done, is for fifty dollars or less, the property must be re-
tained by the mechanic or artisan who ' ' made, repaired, or
altered'''' it, for thirty days, before advertising it for sale.
If the debt be over fifty dollars, the mechanic or artisan
must retain the property for ninety days before advertising
it for sale. The notice, under Sec. 4, must be inserted for
two weeks in some newspaper published in the County
where the work was done ; but, if no newspaper be pub-
lished in the County, then the notice must he posted ^Hn three
of tJie most public places in the county, town or city in which
the worTc may have teen done. The two weeks' notice must
be two weeJcs exclusive of the day of sale.

Note 2d. — "The proceeds of the said sale shall be ap-
plied first to the discharge of the said lien and the expenses
and costs of keeping and selling such property, and the re-
mainder, if any, shall be paid over to the owner thereof.' a
Last clause of Sec. 3.

Remark. — It seems that Sec. 3, does not create any new

AND RAIL ROAD CALCULATOR. 143

lien ; but, is aflu-matory of the lien which the mechanic or
artizan had at common law. And it seems the object of Sec. 3,
is to give a safe and speedy remedy for enforcing the lien.
It seems, therefore, that liens acquired in the cases mention
ed under Sec. 3, need not be filed before a Justice or Sup-
erior Court Clerk, as the mechanic is already in possession
of the property. If the mechanic or artizan parts with the
possession of the property, his right to the remedy, under
Sec. 3, it seems, would be gone. The mechanic or artizan,
under Sec. 3, may file his claim if he chooses so to do.

Note 3d. — It seems that Sections 4 and 5 define the re-
medies to enforce the liens mentioned in Sections 1 and 3,
and may be filed at any tiTne after the materials have been
furnished, the labor performed, &c., and the lien may at-
tach from time of filing. In suits to enforce the lien, be-
fore a justice, the summons should state in addition, the fol-
lowing words, ' ' and for which claim of lien under the Act
was filed before A. B., Esq." It is to be tried by the jus-
tice as any other cause.

Remaek. — No forms are inserted applicable to the Sup-
erior Court, in such cases, counsel learned in the law should
be invariably consulted.

144 THE MAN OF BUSINESS

FORM OF justice's JUDGMENT IN CASES UNDER THE LIEN ACT»-

NoRTH Carolina, ) r r *- •> n *
Chatham County. I -^" " '''^"^' ^''"'•«'

John Den, "]
Plaintiffj \
Against \ Action to enforce lien under Act 1869-70*
Richard Fen,

Defendant. J

In the above entitled cause, it is ordered, adjudged and
decreed, that the plaintiff do recover of the defendant the

sum of dollars and costs to the amount of dollars,

with interest on, &c.

And it is further ordered, adjudged, and decreed, that
the said lien of the plaintiff is valid, and binding upon the
following property of the defendant, to-wit : [here set out
the property upon which the lien attaches^ and that the same
be condemned to be sold to answer the debt and judgment
in this cause.

^ A. B., J. P.

WILLS.

In the name of God, Amen. I, John Den, of sound and
disposing mind and memory, being desirous of settling my
worldly affairs, whilst having the capacity so to do, do de-
clare this to be my last will and testament :

Item 1. It is my will that, i&c.

Item 2. I give, devise, and bequeath unto A. B., &c^
[By items set out the property and to whom given^ <&c.]

Item 3. I appoint and make 0. D., my executor to this,
my last will and testament.

In witness of all which things I have hereunto set my
hand and seal this the — day of , A. D., 187 — .

Signed, sealed and pub-
lished in the presence of
Richard Roe,
John Doe.

AND RAIL EOAD CALCULATOR. 145

Remark. — As the lien law is of great importance to me-
chanics and laborers, it ish ere below appended as found in
*'Laws of North Carolina. Chap. CCVI. 1869-'70.

AN ACT FOE, THE PROTECTION OF MECHANICS AND OTHER
LABORERS, MATERIALS, ETC.

Section 1. The General Assenibly of North Carolina do
enact, That every building built, rebuilt, repaired or im-
proved, toget;her with the necessary lots on which said
building may be situated, and every lot, farm or vessel or
a,ny kind of property not herein enumerated shall be subject
to a lien for the same or material furnished.

Sec. 2. The lien for work on crops or farms or materials
given by this act shall be preferred to every other lien or
incumbrance which attached upon the property subsequent
to the time at which the work was commenced or the mate-
rials were furnished.

Sec. 3. Any mechanic or artlzan who shall make, alter
or repair any article of personal property at the request of
the owner or legal possessor of such property, shall have a
lien on such property so made, altered or repaired for his
just and reasonable charge for his work done and material
furnished, and may hold and retain possession of the same
until such just and reasonable charges shall be paid; and,
if not paid for within the space of thirty days, provided it
does not exceed fifty dollars, if over fifty dollars ninety
days, after the work shall have been done, such mechanic
or artizan may proceed to sell the property so made, alter-
ed or repaired at public auction, by giving two weeks pub-
lic notice of such sale by advertising in some newspaper in

146 THE MAN OF BUSINESS

the county in which the work may have been done, or if
there be no such newspaper, then by posting up notice of
such sale in three of the most public places in the county,
town or city in which the work may have been done, and
the proceeds of the said sale shall be applied first to the
discharge of the said lien and the expenses and costs of
keeping and selling such property, and the remainder, if
any, shall be paid over to the owner thereof.

Sec. 4. All claims under two hundred dollars may be
filed in the office of the nearest magistrate if over twa
hundred dollars, in the office of the superior court clerk in
any county where the labor has been performed or the
material furnished ; but all claims filed shall be in detail,
specifying all materials furnished or labor performed, and
at what date it was performed or material furnished in case
of contract or otherwise. If the parties interested make a
special contract for such labor performed, or if such mate-
rial and labor are specified in writing, in such cases it shall
be decided agreeable to the terms of the contract, provided
the terms of such contract do not effect the lien for such
labor performed or materials furnished.

Sec. 5. In case of any disagreement between the parties
interested in any such contract it may be brought before the
nearest magistrate by the plaintiff or defendant for arbitra-
tion or otherwise, as the magistrate may decide, provided
the amount claimed does not exceed two hundred dollars ;
if over that amount, all claims must be filled with the clerk
of the superior court and entered on the calendar so as to
be brought before the court at the first term after the filing
of any claims. The judges of the superior court may ap-

AND RAIL ROAD CALCULATOR. 147

point referees to ascertain the proper value of any labor
performed on any building or farm, or any material fur-
nished or specified in the application at the time of plaintiff
or defendant filing his petition.

Sec. 6. That nothing contained in this act shall be con-
strued to affect the rights of any person to whom any debt
may be due for any work done which priority of claims
filed with the proper officer.

Sec. 7. Costs are allowed to either party upon the rules
established by law in actions arising or contracts made un-
der the code of civil procedure.

Sec. 8. The defendant in any suit to enforce the lien
shall be entitled to any set off or claim arising between the
contractors during the performance of the contract.

Sec. 9. That all laws or parts of laws coming in coiaflict
with the provisions of this act are hereby repealed.

Sec. 10. That this act shall be in force from and after
its ratification.

Ratified the 38th day of March, A. D. 1870.

North Caroima State Library
Raleigh

ADVERTISEMENT. . I

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W. H. & R S. TUCKER & CO.,

WHOLESALE AND RETAIL

DEALERS AND JOBBERS IN

Jemgtt mi §mmiu §x^ §>$&iU,

Hats, Boots, Shoes, Garpetings, Notions, ^c,
No, 23 and 25 Fayetteville Street,

RALEIGH, N. C.
AN ANALYTICAL

AND

ILLUSTRATIVE AND CONSTRUCTIVE GRAMMAR

ENGLISH LANGUAGE

REV. PROF. BRANTLEY YORK.

IW TWO PARTS.

Accompanied by several original diagrams, exhibiting an
occular illustration of some of the most difficult principles
of the source of language; also, an extensive glossarj*^ of

II ADVERTISEMENT.

the derivation of the principal scientific terms and in this
work.

The plan of teaching, as laid down in this work, is en-
dorsed by the most accomplished teachers in this and other
States. It meets a want long felt in our schools. It simpli-
fies the study of grammar, and leads the student to seek by
the simplest methods, the true Philosophy of Language.

TES7IM0NAL.

Among others, the Rev. A. W. Mangum, A. B., in a re-
view of the work, says :

"But it is Ms Grammar which I wish especially to recomniMid, Those
who are acquainted with the various Grammars of our language will readily
admit that all the pretended new ones, published for the last fifty years
have been little more than copies of the ideas of those before them, with a
change in expression or words and arrangement. I can safely say that
Prof. York's is a new Grammar. It contains originality, and that originality
is unquestionably improvement.

All who have taught or studied English Grammar are aware that general-
ly the memory is the chief, and often the only faculty of the mind exercised
by the learner; but Prof. York's requires especially the exercises of reason,
and thus enables the student to Incorporate its rules and principles into his
thus enables the student to incorporate its rules and principjes into bis
habits of thinking, speaking and writing. Unlike others, he carefully gives
reasons for his rules and principles. He has made it a grand objeci! to
teach the language with the Grammar, thus again outstripping others.

He has given plain, pointed and comprehensive i^ules for punctuation.
Every one knows the diflftoulty of learning to punctuate correctly, and also
how ineflaoient the rules of most authors on punctuation are. Prof. York's
rules are easily understood and truly practical A glossary of all the techni-
cal! terms used is annexed to the volume; a great advantage to the student,
as he seldom knows anything about Latin or Greek.

In fine, the author detects and exposes the imperfectione of others ; ex-
plodes time-honored errors ; establishes new truths; discovers new princi-
ples ; and produces positive and valuable improvements in many respects.
Several distinguished teachers in high sohools in North Carolina have adop-
ted his Grammar as a text book. If it be an improvement on other similar
works, surely others should be discarded and it adopted.

The author is a North Carolinian, and If his book possesses real merit.
North Carolinians ought to encourage his talent and give him their patron-

ADVERTISEMENT.

Ill

S. C. POOL,
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F. O. MORING,
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